<PAGE>

 
                                                                   EXHIBIT 10.9



                      ====================================


                SERIES A CAPITAL SECURITIES GUARANTEE AGREEMENT


                                First USA, Inc.


                         Dated as of December 20, 1996


                      ====================================
<PAGE>
                          TABLE OF CONTENTS
                          -----------------
 
                                                             Page


                             ARTICLE I
                  DEFINITIONS AND INTERPRETATION

     SECTION 1.1  Definitions and Interpretation..............  2

                            ARTICLE II
                        TRUST INDENTURE ACT

     SECTION 2.1  Trust Indenture Act; Application............  6
     SECTION 2.2  Lists of Holders of Securities..............  6
     SECTION 2.3  Reports by the Capital Securities 
                  antee Trustee...............................  6
     SECTION 2.4  Periodic Reports to Capital Securities
                  Guarantee Trustee...........................  7
     SECTION 2.5  Evidence of Compliance with Conditions
                  Precedent...................................  7
     SECTION 2.6  Events of Default; Waiver...................  7
     SECTION 2.7  Event of Default; Notice....................  8
     SECTION 2.8  Conflicting Interests.......................  8

                            ARTICLE III
                   POWERS, DUTIES AND RIGHTS OF
               CAPITAL SECURITIES GUARANTEE TRUSTEE

     SECTION 3.1  Powers and Duties of the Capital Securi-
                  ties Guarantee Trustee......................  8
     SECTION 3.2  Certain Rights of Capital Securities
                  Guarantee Trustee..........................  11
     SECTION 3.3. Not Responsible for Recitals or Issuance
                  of Series A Capital Securities Guarantee.... 13

                            ARTICLE IV
               CAPITAL SECURITIES GUARANTEE TRUSTEE

     SECTION 4.1  Capital Securities Guarantee Trustee;
                  Eligibility................................. 13
     SECTION 4.2  Appointment, Removal and Resignation of
                  Capital Securities Guarantee Trustee........ 14

                             ARTICLE V
                             GUARANTEE

     SECTION 5.1  Guarantee................................... 15
     SECTION 5.2  Waiver of Notice and Demand................. 15
     SECTION 5.3  Obligations Not Affected.................... 15
     SECTION 5.4  Rights of Holders........................... 16
     SECTION 5.5  Guarantee of Payment........................ 17


<PAGE>
 
     SECTION 5.6  Subrogation................................. 17
     SECTION 5.7  Independent Obligations..................... 17

                            ARTICLE VI
             LIMITATION OF TRANSACTIONS; SUBORDINATION

     SECTION 6.1  Limitation of Transactions.................. 18
     SECTION 6.2  Ranking..................................... 19

                            ARTICLE VII
                            TERMINATION

     SECTION 7.1  Termination................................. 19

                           ARTICLE VIII
                          INDEMNIFICATION

     SECTION 8.1  Exculpation................................. 19
     SECTION 8.2  Indemnification............................. 20

                            ARTICLE IX
                           MISCELLANEOUS

     SECTION 9.1  Successors and Assigns...................... 20
     SECTION 9.2  Amendments.................................. 21
     SECTION 9.3  Notices..................................... 21
     SECTION 9.4  Exchange Offer.............................. 22
     SECTION 9.5  Benefit..................................... 22
     SECTION 9.6  Governing Law............................... 22


                                      ii
<PAGE>
 
                SERIES A CAPITAL SECURITIES GUARANTEE AGREEMENT


          This GUARANTEE AGREEMENT (the "Series A Capital Securities
Guarantee"), dated as of December 20, 1996 is executed and delivered by First
USA, Inc., a Delaware corporation (the "Guarantor"), and The Bank of New York,
a New York banking corporation, as trustee (the "Capital Securities Guarantee
Trustee"), for the benefit of the Holders (as defined herein) from time to time
of the Series A Capital Securities (as defined herein) of First USA Capital
Trust I, a Delaware statutory business trust (the "Issuer").

          WHEREAS, pursuant to an Amended and Restated Declaration of Trust
(the "Declaration"), dated as of December 20, 1996 among the trustees of the
Issuer, the Guarantor, as sponsor, and the holders from time to time of
undivided beneficial interests in the assets of the Issuer, the Issuer (i) is
issuing on the date hereof 200,000 capital securities, having an aggregate
liquidation amount of $200,000,000 and (ii) may issue in the future up to a
further 30,000 capital securities, having an aggregate liquidation amount of
$30,000,000 following the exercise of an over-allotment option pursuant to the
Purchase Agreement (as defined in the Declaration), such capital securities
being designated the 9.33% Series A Capital Securities (collectively the
"Series A Capital Securities") and, in connection with an Exchange Offer (as
defined in the Declaration) to execute and deliver the Series B Capital
Securities Guarantee (as defined in the Declaration) for the benefit of holders
of the Series B Capital Securities (as defined in the Declaration).

          WHEREAS, as incentive for the Holders to purchase the Series A Capital
Securities, the Guarantor desires irrevocably and unconditionally to agree, to
the extent set forth in this Series A Capital Securities Guarantee, to pay to
the Holders the Guarantee Payments (as defined below).  The Guarantor agrees to
make certain other payments on the terms and conditions set forth herein.

          WHEREAS, the Guarantor is executing and delivering a guarantee
agreement (the "Common Securities Guarantee"), with substantially identical
terms to this Series A Capital Securities Guarantee, for the benefit of the
holders of the Common Securities (as defined herein), except that if an Event
of Default (as defined in the Declaration) has occurred and is continuing, the
rights of holders of the Common Securities to receive Guarantee Payments under
the Common Securities Guarantee are subordinated, to the extent and in the
manner set forth in the Common Securities Guarantee, to the rights of holders
of Series A Capital Securities and the Series B Capital Securities to receive
Guarantee Payments under this Series A Capital Securities Guarantee and the
Series B Capital Securities Guarantee, as the case may be.
<PAGE>
 
          NOW, THEREFORE, in consideration of the purchase by each Holder, which
purchase the Guarantor hereby acknowledges shall benefit the Guarantor, the
Guarantor executes and delivers this Series A Capital Securities Guarantee for
the benefit of the Holders.


                                   ARTICLE I
                         DEFINITIONS AND INTERPRETATION

SECTION 1.1    Definitions and Interpretation
               ------------------------------

          In this Series A Capital Securities Guarantee, unless the context
otherwise requires:

          (a) Capitalized terms used in this Series A Capital Securities
              Guarantee but not defined in the preamble above have the
              respective meanings assigned to them in this Section 1.1;

          (b) Terms defined in the Declaration as at the date of execution of
              this Series A Capital Securities Guarantee have the same meaning
              when used in this Series A Capital Securities Guarantee unless 
              otherwise defined in this Series A Capital Securities Guarantee;

          (c) a term defined anywhere in this Series A Capital Securities
              Guarantee has the same meaning throughout;

          (d) all references to "the Series A Capital Securities Guarantee" or
              "this Series A Capital Securities Guarantee" are to this Series A
              Capital Securities Guarantee as modified, supplemented or amended
              from time to time;

          (e) all references in this Series A Capital Securities Guarantee to
              Articles and Sections are to Articles and Sections of this Series
              A Capital Securities Guarantee, unless otherwise specified;

          (f) a term defined in the Trust Indenture Act has the same meaning
              when used in this Series A Capital Securities Guarantee, unless
              otherwise defined in this Series A Capital Securities Guarantee or
              unless the context otherwise requires; and

          (g) a reference to the singular includes the plural and vice versa.

                                       2
<PAGE>
 
          "Affiliate" has the same meaning as given to that term in Rule 405
           ---------                                                        
under the Securities Act of 1933, as amended, or any successor rule thereunder.

          "Business Day" means any day other than a Saturday or a Sunday, or a
           ------------                                                       
day on which banking institutions in The City of New York or Wilmington,
Delaware are authorized or required by law or executive order to close.

          "Capital Securities Guarantee Trustee" means The Bank of New York,
           ------------------------------------                             
until a Successor Capital Securities Guarantee Trustee has been appointed and
has accepted such appointment pursuant to the terms of this Series A Capital
Securities Guarantee and thereafter means each such Successor Capital
Securities Guarantee Trustee.

          "Common Securities" means the securities representing common undivided
           -----------------                                                    
beneficial interests in the assets of the Issuer.

          "Corporate Trust Office" means the office of the Capital Securities
           ----------------------                                            
Guarantee Trustee at which the corporate trust business of the Capital
Securities Guarantee Trustee shall, at any particular time, be principally
administered, which office at the date of execution of this Agreement is located
at 101 Barclay Street, 21 West, New York, New York 10286.

          "Covered Person" means any Holder or beneficial owner of Series A
           --------------                                                  
Capital Securities.

          "Debentures" means the series of subordinated debt securities of the
           ----------                                                         
Guarantor designated the 9.33% Series A Junior Subordinated Deferrable Interest
Debentures due January 15, 2027 held by the Property Trustee (as defined in the
Declaration) of the Issuer.

          "Event of Default" means a default by the Guarantor on any of its
           ----------------                                                
payment or other obligations under this Series A Capital Securities Guarantee.

          "Guarantee Payments" means the following payments or distributions,
           ------------------                                                
without duplication, with respect to the Series A Capital Securities, to the
extent not paid or made by the Issuer:  (i) any accumulated and unpaid
Distributions (as defined in the Declaration) that are required to be paid on
such Series A Capital Securities to the extent the Issuer has funds on hand
legally available therefor at such time, (ii) the redemption price, including
all accumulated and unpaid Distributions to the date of redemption (the
"Redemption Price") to the extent the Issuer has funds on hand legally available
therefor at such time, with respect to any Series A Capital Securities called
for redemption by the Issuer, and (iii) upon a voluntary or involuntary termina-

                                       3
<PAGE>
 
tion and liquidation of the Issuer (other than in connection with the
distribution of Debentures to the Holders in exchange for Series A Capital
Securities as provided in the Declaration), the lesser of (a) the aggregate of
the liquidation amount and all accumulated and unpaid Distributions on the
Series A Capital Securities to the date of payment, to the extent the Issuer has
funds on hand legally available therefor, and (b) the amount of assets of the
Issuer remaining available for distribution to Holders in liquidation of the
Issuer. If an Event of Default has occurred and is continuing, no Guarantee
Payments under the Common Securities Guarantee with respect to the Common
Securities or any guarantee payment under any Other Common Securities Guarantees
shall be made until the Holders shall be paid in full the Guarantee Payments to
which they are entitled under this Series A Capital Securities Guarantee.

          "Holder" shall mean any holder, as registered on the books and records
           ------                                                               
of the Issuer, of any Series A Capital Securities; provided, however, that, in
determining whether the holders of the requisite percentage of Series A Capital
Securities have given any request, notice, consent or waiver hereunder, "Holder"
shall not include the Guarantor or any Affiliate of the Guarantor.

          "Indemnified Person" means the Capital Securities Guarantee Trustee,
           ------------------                                                 
any Affiliate of the Capital Securities Guarantee Trustee, or any officers,
directors, shareholders, members, partners, employees, representatives,
nominees, custodians or agents of the Capital Securities Guarantee Trustee.

          "Indenture" means the Indenture dated as of December 20, 1996, among
           ---------                                                          
the Guarantor (the "Debenture Issuer") and The Bank of New York, as trustee,
pursuant to which the Debentures are to be issued to the Property Trustee of the
Issuer.

          "Majority in liquidation amount of the Series A Capital Securities"
           ----------------------------------------------------------------- 
means, except as provided by the Trust Indenture Act, a vote by Holder(s) of
Series A Capital Securities, voting separately as a class, of more than 50% of
the aggregate liquidation amount (including the stated amount that would be paid
on redemption, liquidation or otherwise, plus accumulated and unpaid
Distributions to the date upon which the voting percentages are determined) of
all Series A Capital Securities.

          "Officers' Certificate" means, with respect to any person, a
           ---------------------                                      
certificate signed by the Chairman, a Vice Chairman, the Chief Executive
Officer, the President, a Vice President, the Comptroller, the Group Director,
Asset/Liability Management, the Clerk or an Assistant Clerk, the Secretary or an
Assistant Secre tary of the Guarantor.  Any Officers' Certificate delivered with
respect to compliance with a condition or covenant provided for in this Series A
Capital Securities Guarantee shall include:

                                       4
<PAGE>
 
     (h)  a statement that each officer signing the Officers' Certificate has
read the covenant or condition and the definitions relating thereto;

     (i) a statement that each such officer has made such examination or
investigation as, in such officer's opinion, is necessary to enable such officer
to express an informed opinion as to whether or not such covenant or condition
has been complied with; and

     (j) a statement as to whether, in the opinion of each such officer, such
condition or covenant has been complied with.

          "Other Common Securities Guarantees" shall have the same meaning as
           ----------------------------------                                
"Other Guarantees" in the Common Securities Guarantee.

          "Other Debentures" means all junior subordinated debentures issued by
           ----------------                                                    
the Guarantor from time to time and sold to trusts to be established by the
Guarantor (if any), in each case similar to the Issuer.

          "Other Guarantees" means all guarantees issued by the Guarantor with
           ----------------                                                   
respect to capital securities (if any) similar to the Series A Capital
Securities issued by other trusts to be established by the Guarantor (if any),
in each case similar to the Issuer.

          "Person" means a legal person, including any individual, corporation,
           ------                                                               
estate, partnership, joint venture, association, joint stock company, limited
liability company, trust, unincorporated association, or government or any
agency or political subdivision thereof, or any other entity of whatever nature.

          "Registration Rights Agreement"  means the Registration Rights
           -----------------------------                                
Agreement, dated as of December 20, 1996, by and among the Guarantor, the Issuer
and the Initial Purchasers named therein as such agreement may be amended,
modified or supplemented from time to time.

          "Responsible Officer" means, with respect to the Capital Securities
           -------------------                                               
Guarantee Trustee, any officer within the Corporate Trust Office of the Capital
Securities Guarantee Trustee, including any vice president, any assistant vice
president, any assistant secretary, the treasurer, any assistant treasurer or
other officer of the Corporate Trust Office of the Capital Securities Guarantee
Trustee customarily performing functions similar to those performed by any of
the above designated officers and also means, with respect to a particular
corporate trust matter, any other officer to whom such matter is

                                       5
<PAGE>
 
referred because of that officer's knowledge of and familiarity with the
particular subject.

          "Successor Capital Securities Guarantee Trustee" means a successor
           ----------------------------------------------                   
Capital Securities Guarantee Trustee possessing the qualifications to act as
Capital Securities Guarantee Trustee under Section 4.1.

          "Trust Indenture Act" means the Trust Indenture Act of 1939, as
           -------------------                                           
amended.

          "Trust Securities" means the Common Securities and the Series A
           ----------------                                              
Capital Securities and Series B Capital Securities, collectively.


                                   ARTICLE II
                              TRUST INDENTURE ACT

SECTION 2.1    Trust Indenture Act; Application
               --------------------------------

          (a) This Series A Capital Securities Guarantee is subject to the
provisions of the Trust Indenture Act that are required to be part of this
Series A Capital Securities Guarantee and shall, to the extent applicable, be
governed by such provisions; and

          (b) if and to the extent that any provision of this Series A Capital
Securities Guarantee limits, qualifies or conflicts with the duties imposed by
Section 310 to 317, inclusive, of the Trust Indenture Act, such imposed duties
shall control.

SECTION 2.2    Lists of Holders of Securities
               ------------------------------

          (a) The Guarantor shall provide the Capital Securities Guarantee
Trustee (unless the Capital Securities Guarantee Trustee is otherwise the
registrar of the Capital Securities) with a list, in such form as the Capital
Securities Guarantee Trustee may reasonably require, of the names and addresses
of the Holders of the Series A Capital Securities ("List of Holders") as of such
date, (i) within one Business Day after June 1 and December 1 of each year, and
(ii) at any other time within 30 days of receipt by the Guarantor of a written
request for a List of Holders as of a date no more than 14 days before such List
of Holders is given to the Capital Securities Guarantee Trustee provided, that
                                                                --------      
the Guarantor shall not be obligated to provide such List of Holders at any time
the List of Holders does not differ from the most recent List of Holders given
to the Capital Securities Guarantee Trustee by the Guarantor. The Capital
Securities Guarantee Trustee may destroy any List of Holders previously given to
it on receipt of a new List of Holders.

                                       6
<PAGE>
 
          (b) The Capital Securities Guarantee Trustee shall comply with its
obligations under Sections 311(a), 311(b) and Section 312(b) of the Trust
Indenture Act.

SECTION 2.3    Reports by the Capital Securities Guarantee Trustee
               ----------------------------------------------------

          Within 60 days after December 15 of each year, commencing December
15, 1997, the Capital Securities Guarantee Trustee shall provide to the Holders
such reports as are required by Section 313 of the Trust Indenture Act, if any,
in the form and in the manner provided by Section 313 of the Trust Indenture
Act. The Capital Securities Guarantee Trustee shall also comply with the
requirements of Section 313(d) of the Trust Indenture Act.

SECTION 2.4    Periodic Reports to Capital Securities Guarantee Trustee
               --------------------------------------------------------

          The Guarantor shall provide to the Capital Securities Guarantee
Trustee such documents, reports and information as required by Section 314 (if
any) and the compliance certificate required by Section 314 of the Trust
Indenture Act in the form, in the manner and at the times required by Section
314 of the Trust Indenture Act.  Delivery of such reports, information and
documents to the Capital Securities Guarantee Trustee is for informational
purposes only and the Capital Securities Guarantee Trustee's receipt of such
shall not constitute constructive notice of any information contained therein or
determinable from information contained therein, including the Guarantor's
compliance with any of its covenants hereunder (as to which the Capital
Securities Guarantee Trustee is entitled to rely exclusively on Officers'
Certificates).

SECTION 2.5    Evidence of Compliance with Conditions Precedent
               ------------------------------------------------

          The Guarantor shall provide to the Capital Securities Guarantee
Trustee such evidence of compliance with any conditions precedent, if any,
provided for in this Series A Capital Securities Guarantee that relate to any
of the matters set forth in Section 314(c) of the Trust Indenture Act.  Any
certificate or opinion required to be given by an officer pursuant to Section
314(c)(1) may be given in the form of an Officers' Certificate.

SECTION 2.6    Events of Default; Waiver
               -------------------------

          The Holders of a Majority in liquidation amount of Series A Capital
Securities may, by vote, on behalf of all of the Holders, waive any past Event
of Default and its consequences.  Upon such waiver, any such Event of Default
shall cease to exist, and any Event of Default arising therefrom shall be deemed
to have been cured, for every purpose of this Series A Capital Securities
Guarantee, but no such waiver shall extend to any

                                       7
<PAGE>
 
subsequent or other default or Event of Default or impair any right consequent
thereon.

SECTION 2.7    Event of Default; Notice
               ------------------------

          (a) The Capital Securities Guarantee Trustee shall, within 90 days
after the occurrence of a default with respect to this Capital Securities
Guarantee, mail by first class postage prepaid, to all Holders, notices of all
defaults actually known to a Responsible Officer of the Capital Securities
Guarantee Trustee, unless such defaults have been cured before the giving of
such notice, provided, that, except in the case of default in the payment of any
Guarantee Payment, the Capital Securities Guarantee Trustee shall be protected
in withholding such notice if and so long as the board of directors, the
executive committee, or a trust committee of directors and/or Responsible
Officer in good faith determines that the withholding of such notice is in the
interests of the Holders.

          (b) The Capital Securities Guarantee Trustee shall not be deemed to
have knowledge of any Event of Default unless the Capital Securities Guarantee
Trustee shall have received written notice, or a Responsible Officer charged
with the administration of the Declaration shall have obtained actual knowledge,
of such Event of Default.

SECTION 2.8    Conflicting Interests
               ---------------------

          The Declaration shall be deemed to be specifically described in this
Series A Capital Securities Guarantee for the purposes of clause (i) of the
first proviso contained in Section 310(b) of the Trust Indenture Act.


                                  ARTICLE III
                          POWERS, DUTIES AND RIGHTS OF
                      CAPITAL SECURITIES GUARANTEE TRUSTEE

SECTION 3.1    Powers and Duties of the Capital Securities Guarantee Trustee
               --------------------------------------------------------------

          (a) This Series A Capital Securities Guarantee shall be held by the
Capital Securities Guarantee Trustee for the benefit of the Holders, and the
Capital Securities Guarantee Trustee shall not transfer this Series A Capital
Securities Guarantee to any Person except a Holder exercising his or her rights
pursuant to Section 5.4(b) or to a Successor Capital Securities Guarantee
Trustee on acceptance by such Successor Capital Securities Guarantee Trustee of
its appointment to act as Successor Capital Securities Guarantee Trustee. The
right, title and interest of the Capital Securities Guarantee Trustee shall
automatically vest in any Successor Capital Securities Guarantee Trustee, and
such

                                       8
<PAGE>
 
vesting and succession of title shall be effective whether or not conveyancing
documents have been executed and delivered pursuant to the appointment of such
Successor Capital Securities Guarantee Trustee.

          (b) If an Event of Default actually known to a Responsible Officer
has occurred and is continuing, the Capital Securities Guarantee Trustee shall
enforce this Series A Capital Securities Guarantee for the benefit of the
Holders.

          (c) The Capital Securities Guarantee Trustee, before the occurrence of
any Event of Default and after the curing of all Events of Default that may have
occurred, shall undertake to perform only such duties as are specifically set
forth in this Series A Capital Securities Guarantee, and no implied covenants
shall be read into this Series A Capital Securities Guarantee against the
Capital Securities Guarantee Trustee. In case an Event of Default has occurred
(that has not been cured or waived pursuant to Section 2.6) and is actually
known to a Responsible Officer, the Capital Securities Guarantee Trustee shall
exercise such of the rights and powers vested in it by this Series A Capital
Securities Guarantee, and use the same degree of care and skill in its exercise
thereof, as a prudent person would exercise or use under the circumstances in
the conduct of his or her own affairs.

          (d) No provision of this Series A Capital Securities Guarantee shall
be construed to relieve the Capital Securities Guarantee Trustee from liability
for its own negligent action, its own negligent failure to act, or its own
willful misconduct, except that:

     (i) prior to the occurrence of any Event of Default and after the curing or
waiving of all such Events of Default that may have occurred:

          (A) the duties and obligations of the Capital Securities Guarantee
     Trustee shall be determined solely by the express provisions of this Series
     A Capital Securities Guarantee, and the Capital Securities Guarantee
     Trustee shall not be liable except for the performance of such duties and
     obligations as are specifically set forth in this Series A Capital
     Securities Guarantee, and no implied covenants or obligations shall be read
     into this Series A Capital Securities Guarantee against the Capital
     Securities Guarantee Trustee; and

          (B) in the absence of bad faith on the part of the Capital Securities
     Guarantee Trustee, the Capital Securities Guarantee Trustee may
     conclusively rely, as to the truth of the statements and the correctness of

                                       9
<PAGE>
 
     the opinions expressed therein, upon any certificates or opinions furnished
     to the Capital Securities Guarantee Trustee and conforming to the
     requirements of this Series A Capital Securities Guarantee; but in the case
     of any such certificates or opinions that by any provision hereof are
     specifically required to be furnished to the Capital Securities Guarantee
     Trustee, the Capital Securities Guarantee Trustee shall be under a duty to
     examine the same to determine whether or not they conform to the
     requirements of this Series A Capital Securities Guarantee;

     (ii) the Capital Securities Guarantee Trustee shall not be liable for any
error of judgment made in good faith by a Responsible Officer, unless it shall
be proved that the Capital Securities Guarantee Trustee was negligent in 
ascertaining the pertinent facts upon which such judgment was made;

     (iii) the Capital Securities Guarantee Trustee shall not be liable with
respect to any action taken or omitted to be taken by it in good faith in
accordance with the direction of the Holders of a Majority in liquidation
amount of the Series A Capital Securities relating to the time, method and place
of conducting any proceeding for any remedy available to the Capital Securities
Guarantee Trustee, or exercising any trust or power conferred upon the Capital
Securities Guarantee Trustee under this Series A Capital Securities Guarantee;
and

     (iv) no provision of this Series A Capital Securities Guarantee shall
require the Capital Securities Guarantee Trustee to expend or risk its own funds
or otherwise incur personal financial liability in the performance of any of its
duties or in the exercise of any of its rights or powers, if the Capital
Securities Guarantee Trustee shall have reasonable grounds for believing that
the repayment of such funds or liability is not reasonably assured to it under
the terms of this Series A Capital Securities Guarantee or indemnity, reasonably
satisfactory to the Capital Securities Guarantee Trustee, against such risk or
liability is not reasonably assured to it.

SECTION 3.2    Certain Rights of Capital Securities Guarantee Trustee
               ------------------------------------------------------

          (a) Subject to the provisions of Section 3.1:

     (i)  The Capital Securities Guarantee Trustee may conclusively rely, and
shall be fully protected in acting or refraining from acting, upon any
resolution, certificate, statement, instrument, opinion, report, notice,
request,

                                       10
<PAGE>
 
direction, consent, order, bond, debenture, note, other evidence of indebtedness
or other paper or document believed by it to be genuine and to have been signed,
sent or presented by the proper party or parties.

     (ii)  Any direction or act of the Guarantor contemplated by this Series A
Capital Securities Guarantee may be sufficiently evidenced by an Officers'
Certificate.

     (iii)  Whenever, in the administration of this Series A Capital Securities
Guarantee, the Capital Securities Guarantee Trustee shall deem it desirable
that a matter be proved or established before taking, suffering or omitting any
action hereunder, the Capital Securities Guarantee Trustee (unless other
evidence is herein specifically prescribed) may, in the absence of bad faith on
its part, request and conclusively rely upon an Officers' Certificate which,
upon receipt of such request, shall be promptly delivered by the Guarantor.

     (iv)  The Capital Securities Guarantee Trustee shall have no duty to see to
any recording, filing or registration of any instrument (or any rerecording,
refiling or registration thereof).

     (v)  The Capital Securities Guarantee Trustee may consult with counsel of
its selection, and the advice or opinion of such counsel with respect to legal
matters shall be full and complete authorization and protection in respect of
any action taken, suffered or omitted by it hereunder in good faith and in
accordance with such advice or opinion. Such counsel may be counsel to the
Guarantor or any of its Affiliates and may include any of its employees.  The
Capital Securities Guarantee Trustee shall have the right at any time to seek
instructions concerning the administration of this Series A Capital Securities
Guarantee from any court of competent jurisdiction.

     (vi)  The Capital Securities Guarantee Trustee shall be under no obligation
to exercise any of the rights or powers vested in it by this Series A Capital
Securities Guarantee at the request or direction of any Holder, unless such
Holder shall have provided to the Capital Securities Guarantee Trustee such
security and indemnity, reasonably satisfactory to the Capital Securities
Guarantee Trustee, against the costs, expenses (including attorneys' fees and
expenses and the expenses of the Capital Securities Guarantee Trustee's agents,
nominees or custodians) and liabilities that might be incurred by it in
complying with such request or direction, including such reasonable advances as
may be requested by the Capital Securities Guarantee Trustee; provided that,
nothing contained in this Section 3.2(a)(vi)

                                       11
<PAGE>
 
shall be taken to relieve the Capital Securities Guarantee Trustee, upon the
occurrence of an Event of Default, of its obligation to exercise the rights and
powers vested in it by this Series A Capital Securities Guarantee.

     (vii)  The Capital Securities Guarantee Trustee shall not be bound to make
any investigation into the facts or matters stated in any resolution,
certificate, statement, instrument, opinion, report, notice, request, direction,
consent, order, bond, debenture, note, other evidence of indebtedness or other
paper or document, but the Capital Securities Guarantee Trustee, in its
discretion, may make such further inquiry or investigation into such facts or
matters as it may see fit.

     (viii)  The Capital Securities Guarantee Trustee may execute any of the
trusts or powers hereunder or perform any duties hereunder either directly or by
or through agents, nominees, custodians or attorneys, and the Capital 
Securities Guarantee Trustee shall not be responsible for any misconduct or
negligence on the part of any agent or attorney appointed with due care by it
hereunder.

     (ix)  Any action taken by the Capital Securities Guarantee Trustee or its
agents hereunder shall bind the Holders, and the signature of the Capital
Securities Guarantee Trustee or its agents alone shall be sufficient and
effective to perform any such action. No third party shall be required to
inquire as to the authority of the Capital Securities Guarantee Trustee to so
act or as to its compliance with any of the terms and provisions of this Series
A Capital Securities Guarantee, both of which shall be conclusively evidenced
by the Capital Securities Guarantee Trustee's or its agent's taking such action.

     (x)  Whenever in the administration of this Series A Capital Securities
Guarantee the Capital Securities Guarantee Trustee shall deem it desirable to
receive instructions with respect to enforcing any remedy or right or taking any
other action hereunder, the Capital Securities Guarantee Trustee (i) may request
instructions from the Holders of a Majority in liquidation amount of the Series
A Capital Securities, (ii) may refrain from enforcing such remedy or right or
taking such other action until such instructions are received, and (iii) shall
be protected in conclusively relying on or acting in accordance with such
instructions.

     (xi)  The Capital Securities Guarantee Trustee shall not be liable for any
action taken, suffered, or omitted to be taken by it in good faith, without
negligence, and reasonably believed by it to be authorized or within the dis-

                                       12
<PAGE>
 
cretion or rights or powers conferred upon it by this Series A Capital
Securities Guarantee.

          (b) No provision of this Series A Capital Securities Guarantee shall
be deemed to impose any duty or obligation on the Capital Securities Guarantee
Trustee to perform any act or acts or exercise any right, power, duty or
obligation conferred or imposed on it in any jurisdiction in which it shall be
illegal, or in which the Capital Securities Guarantee Trustee shall be
unqualified or incompetent in accordance with applicable law, to perform any
such act or acts or to exercise any such right, power, duty or obligation.  No
permissive power or authority available to the Capital Securities Guarantee
Trustee shall be construed to be a duty.

SECTION 3.3.   Not Responsible for Recitals or Issuance of Series A Capital
               ------------------------------------------------------------
               Securities Guarantee
               --------------------

          The recitals contained in this Series A Capital Securities Guarantee
shall be taken as the statements of the Guarantor, and the Capital Securities
Guarantee Trustee does not assume any responsibility for their correctness.  The
Capital Securities Guarantee Trustee makes no representation as to the validity
or sufficiency of this Series A Capital Securities Guarantee.


                                   ARTICLE IV
                      CAPITAL SECURITIES GUARANTEE TRUSTEE

SECTION 4.1    Capital Securities Guarantee Trustee; Eligibility
               -------------------------------------------------

          (a) There shall at all times be a Capital Securities Guarantee Trustee
which shall:

     (i) not be an Affiliate of the Guarantor; and

     (ii) be a corporation organized and doing business under the laws of the
United States of America or any State or Territory thereof or of the District of
Columbia, or a corporation or Person permitted by the Securities and Exchange
Commission to act as an institutional trustee under the Trust Indenture Act,
authorized under such laws to exercise corporate trust powers, having a combined
capital and surplus of at least 50 million U.S. dollars ($50,000,000), and
subject to supervision or examination by Federal, State, Territorial or District
of Columbia authority.  If such corporation publishes reports of condition at
least annually, pursuant to law or to the requirements of the supervising or
examining authority referred to above, then, for the purposes of this Section
4.1(a)(ii), the combined capital and surplus of such corporation shall be

                                       13
<PAGE>

 
deemed to be its combined capital and surplus as set forth in its most recent
report of condition so published.

          (b) If at any time the Capital Securities Guarantee Trustee shall
cease to be eligible to so act under Section 4.1(a), the Capital Securities
Guarantee Trustee shall immediately resign in the manner and with the effect
set out in Section 4.2(c).

          (c) If the Capital Securities Guarantee Trustee has or shall acquire
any "conflicting interest" within the meaning of Section 310(b) of the Trust
Indenture Act, the Capital Securities Guarantee Trustee and Guarantor shall in
all respects comply with the provisions of Section 310(b) of the Trust Indenture
Act.

SECTION 4.2    Appointment, Removal and Resignation of Capital Securities
               ----------------------------------------------------------
          Guarantee Trustee
          -----------------

          (a) Subject to Section 4.2(b), the Capital Securities Guarantee
Trustee may be appointed or removed without cause at any time by the Guarantor
except during an Event of Default.

          (b) The Capital Securities Guarantee Trustee shall not be removed in
accordance with Section 4.2(a) until a Successor Capital Securities Guarantee
Trustee has been appointed and has accepted such appointment by written
instrument executed by such Successor Capital Securities Guarantee Trustee and
delivered to the Guarantor.

          (c) The Capital Securities Guarantee Trustee shall hold office until a
Successor Capital Securities Guarantee Trustee shall have been appointed or
until its removal or resignation. The Capital Securities Guarantee Trustee may
resign from office (without need for prior or subsequent accounting) by an
instrument in writing executed by the Capital Securities Guarantee Trustee and
delivered to the Guarantor, which resignation shall not take effect until a
Successor Capital Securities Guarantee Trustee has been appointed and has
accepted such appointment by instrument in writing executed by such Successor
Capital Securities Guarantee Trustee and delivered to the Guarantor and the
resigning Capital Securities Guarantee Trustee.

          (d) If no Successor Capital Securities Guarantee Trustee shall have
been appointed and accepted appointment as provided in this Section 4.2 within
60 days after delivery of an instrument of removal or resignation, the Capital
Securities Guarantee Trustee resigning or being removed may petition any court
of competent jurisdiction for appointment of a Successor Capital Securities
Guarantee Trustee.  Such court may thereupon, after prescribing such notice, if
any, as it may deem proper, appoint a Successor Capital Securities Guarantee
Trustee.

                                       14
<PAGE>
 
          (e) No Capital Securities Guarantee Trustee shall be liable for the
acts or omissions to act of any Successor Capital Securities Guarantee Trustee.

          (f) Upon termination of this Series A Capital Securities Guarantee or
removal or resignation of the Capital Securities Guarantee Trustee pursuant to
this Section 4.2, the Guarantor shall pay to the Capital Securities Guarantee
Trustee all amounts due to the Capital Securities Guarantee Trustee accrued to
the date of such termination, removal or resignation.


                                   ARTICLE V
                                   GUARANTEE

SECTION 5.1    Guarantee
               ---------

          The Guarantor irrevocably and unconditionally agrees to pay in full to
the Holders the Guarantee Payments (without duplication of amounts theretofore
paid by the Issuer), as and when due, regardless of any defense, right of set-
off or counterclaim that the Issuer may have or assert.  The Guarantor's
obligation to make a Guarantee Payment may be satisfied by direct payment of the
required amounts by the Guarantor to the Holders or by causing the Issuer to pay
such amounts to the Holders.

SECTION 5.2    Waiver of Notice and Demand
               ---------------------------

          The Guarantor hereby waives notice of acceptance of this Series A
Capital Securities Guarantee and of any liability to which it applies or may
apply, presentment, demand for payment, any right to require a proceeding first
against the Issuer or any other Person before proceeding against the Guarantor,
protest, notice of nonpayment, notice of dishonor, notice of redemption and all
other notices and demands.

SECTION 5.3    Obligations Not Affected
               ------------------------

          The obligations, covenants, agreements and duties of the Guarantor
under this Series A Capital Securities Guarantee shall in no way be affected or
impaired by reason of the happening from time to time of any of the following:

          (a) the release or waiver, by operation of law or otherwise, of the
performance or observance by the Issuer of any express or implied agreement,
covenant, term or condition relating to the Series A Capital Securities to be
performed or observed by the Issuer;

          (b) the extension of time for the payment by the Issuer of all or any
portion of the Distributions, Redemption Price, Liquidation Distribution or any
other sums payable under

                                       15
<PAGE>

 
the terms of the Series A Capital Securities or the extension of time for the
performance of any other obligation under, arising out of, or in connection
with, the Series A Capital Securities (other than an extension of time for
payment of Distributions, Redemption Price, Liquidation Distribution or other
sum payable that results from the extension of any interest payment period on
the Debentures permitted by the Indenture);

          (c) any failure, omission, delay or lack of diligence on the part of
the Holders to enforce, assert or exercise any right, privilege, power or remedy
conferred on the Holders pursuant to the terms of the Series A Capital
Securities, or any action on the part of the Issuer granting indulgence or
extension of any kind;

          (d) the voluntary or involuntary liquidation, dissolution, sale of
any collateral, receivership, insolvency, bankruptcy, assignment for the
benefit of creditors, reorganization, arrangement, composition or readjustment
of debt of, or other similar proceedings affecting, the Issuer or any of the
assets of the Issuer;

          (e) any invalidity of, or defect or deficiency in, the Series A
Capital Securities;

          (f) the settlement or compromise of any obligation guaranteed hereby
or hereby incurred;

          (g)  the consummation of the Exchange Offer; or

          (h) any other circumstance whatsoever that might otherwise constitute
a legal or equitable discharge or defense of a guarantor, it being the intent of
this Section 5.3 that the obligations of the Guarantor with respect to the
Guarantee Payments shall be absolute and unconditional under any and all
circumstances.

          There shall be no obligation of the Holders to give notice to, or
obtain consent of, the Guarantor with respect to the happening of any of the
foregoing.

SECTION 5.4    Rights of Holders
               -----------------

          (a) The Holders of a Majority in liquidation amount of the Series A
Capital Securities have the right to direct the time, method and place of
conducting any proceeding for any remedy available to the Capital Securities
Guarantee Trustee in respect of this Series A Capital Securities Guarantee or
exercising any trust or power conferred upon the Capital Securities Guarantee
Trustee under this Series A Capital Securities Guarantee.

                                       16
<PAGE>

 
          (b) If the Capital Securities Guarantee Trustee fails to enforce such
Series A Capital Securities Guarantee, any Holder may institute a legal
proceeding directly against the Guarantor to enforce the Capital Securities
Guarantee Trustee's rights under this Series A Capital Securities Guarantee,
without first instituting a legal proceeding against the Issuer, the Capital
Securities Guarantee Trustee or any other person or entity. The Guarantor
waives any right or remedy to require that any action be brought first against
the Issuer or any other person or entity before proceeding directly against the
Guarantor.

SECTION 5.5    Guarantee of Payment
               --------------------

          This Series A Capital Securities Guarantee creates a guarantee of
payment and not of collection.

SECTION 5.6    Subrogation
               -----------

          The Guarantor shall be subrogated to all (if any) rights of the
Holders against the Issuer in respect of any amounts paid to such Holders by the
Guarantor under this Series A Capital Securities Guarantee; provided, however,
that the Guarantor shall not (except to the extent required by mandatory 
provisions of law) be entitled to enforce or exercise any right that it may
acquire by way of subrogation or any indemnity, reimbursement or other
agreement, in all cases as a result of payment under this Series A Capital
Securities Guarantee, if, at the time of any such payment, any amounts are due
and unpaid under this Series A Capital Securities Guarantee. If any amount shall
be paid to the Guarantor in violation of the preceding sentence, the Guarantor
agrees to hold such amount in trust for the Holders and to pay over such amount
to the Holders.

SECTION 5.7    Independent Obligations
               -----------------------

          The Guarantor acknowledges that its obligations hereunder are
independent of the obligations of the Issuer with respect to the Series A
Capital Securities, and that the Guarantor shall be liable as principal and as
debtor hereunder to make Guarantee Payments pursuant to the terms of this Series
A Capital Securities Guarantee notwithstanding the occurrence of any event
referred to in subsections (a) through (h), inclusive, of Section 5.3 hereof.


                                   ARTICLE VI
                   LIMITATION OF TRANSACTIONS; SUBORDINATION

SECTION 6.1    Limitation of Transactions
               --------------------------

          So long as any Capital Securities remain outstanding, the Guarantor
shall not (i) declare or pay any dividends or

                                       17
<PAGE>
 
distributions on, or redeem, purchase, acquire, or make a liquidation payment
with respect to, any of the Guarantor's capital stock (which includes common and
preferred stock) or (ii) make any payment of principal, interest or premium, if
any, on or repay or repurchase or redeem any debt securities of the Guarantor
(including any Other Debentures) that rank pari passu with or junior in right of
payment to the Debentures or (iii) make any guarantee payments with respect to
any guarantee by the Guarantor of the debt securities of any subsidiary of the
Guarantor (including Other Guarantees) if such guarantee ranks pari passu or
junior in right of payment to the Debentures (other than (a) dividends or
distributions in shares of, or options, warrants, rights to subscribe for or
purchase shares of, common stock of the Guarantor, (b) any declaration of a
dividend in connection with the implementation of a stockholder's rights plan,
or the issuance of stock under any such plan in the future, or the redemption or
repurchase of any such rights pursuant thereto, (c) payments under the Capital
Securities Guarantee, (d) as a result of a reclassification of the Guarantor's
capital stock or the exchange or the conversion of one class or series of the
Guarantor's capital stock for another class or series of the Guarantor's capital
stock, (e) the purchase of fractional interests in shares of the Guarantor's
capital stock pursuant to the conversion or exchange provisions of such capital
stock or the security being converted or exchanged, and (f) purchases of common
stock related to the issuance of common stock or rights under any of the
Guarantor's benefit plans for its directors, officers or employees or any of the
Guarantor's dividend reinvestment plans) if at such time (i) there shall have
occurred any event of which the Guarantor has actual knowledge that (a) is, or
with the giving of notice or the lapse of time, or both, would be an Event of
Default and (b) in respect of which the Guarantor shall not have taken
reasonable steps to cure, (ii) if such Debentures are held by the Property
Trustee, the Guarantor shall be in default with respect to its payment of any
obligations under this Series A Capital Securities Guarantee or (iii) the
Guarantor shall have given notice of its election of the exercise of its right
to extend the interest payment period pursuant to Section 16.01 of the Indenture
and any such extension shall be continuing.

SECTION 6.2    Ranking
               -------

          This Series A Capital Securities Guarantee will constitute an
unsecured obligation of the Guarantor and will rank (i) subordinate and junior
in right of payment to Senior Indebtedness (as defined in the Indenture), to
the same extent and in the same manner that the Debentures are subordinated to
Senior Indebtedness pursuant to the Indenture (except as indicated below), it
being understood that the terms of Article XV of the Indenture shall apply to
the obligations of the Guarantor under this Series A Capital Securities
Guarantee as if (x) such Article

                                       18
<PAGE>

 
XV were set forth herein in full and (y) such obligations were substituted for
the term "Securities" appearing in such Article XV, except that with respect to
Section 15.03 of the Indenture only, the term "Senior Indebtedness" shall mean
all liabilities of the Guarantor, whether or not for money borrowed (other than
obligations in respect of Other Guarantees), (ii) pari passu with the most
senior preferred or preference stock now or hereafter issued by the Guarantor
and with any Other Guarantee (as defined herein) and any Other Common Securities
Guarantee and any guarantee now or hereafter entered into by the Guarantor in
respect of any preferred or preference stock of any Affiliate of the Guarantor,
and (iii) senior to the Guarantor's common stock.


                                  ARTICLE VII
                                  TERMINATION

SECTION 7.1    Termination
               -----------

          This Series A Capital Securities Guarantee shall terminate (i) upon
full payment of the Redemption Price (as defined in the Declaration) of all
Series A Capital Securities, or (ii) upon liquidation of the Issuer, the full
payment of the amounts payable in accordance with the Declaration or the
distribution of the Debentures to all of the Holders.  Notwithstanding the
foregoing, this Series A Capital Securities Guarantee will continue to be
effective or will be reinstated, as the case may be, if at any time any Holder
must restore payment of any sums paid under the Series A Capital Securities or
under this Series A Capital Securities Guarantee.


                                  ARTICLE VIII
                                INDEMNIFICATION

SECTION 8.1    Exculpation
               -----------

          (a) No Indemnified Person shall be liable, responsible or accountable
in damages or otherwise to the Guarantor or any Covered Person for any loss,
damage or claim incurred by reason of any act or omission performed or omitted
by such Indemnified Person in good faith in accordance with this Series A
Capital Securities Guarantee and in a manner that such Indemnified Person
reasonably believed to be within the scope of the authority conferred on such
Indemnified Person by this Series A Capital Securities Guarantee or by law,
except that an Indemnified Person shall be liable for any such loss, damage or
claim incurred by reason of such Indemnified Person's negligence or willful
misconduct with respect to such acts or omissions.

          (b) An Indemnified Person shall be fully protected in relying in good
faith upon the records of the Guarantor and upon

                                       19
<PAGE>
 
such information, opinions, reports or statements presented to the Guarantor by
any Person as to matters the Indemnified Person reasonably believes are within
such other Person's professional or expert competence and who has been selected
with reasonable care by or on behalf of the Guarantor, including information,
opinions, reports or statements as to the value and amount of the assets,
liabilities, profits, losses, or any other facts pertinent to the existence and
amount of assets from which Distributions to Holders of Series A Capital
Securities might properly be paid.

SECTION 8.2    Indemnification
               ---------------

          The Guarantor agrees to indemnify each Indemnified Person for, and to
hold each Indemnified Person harmless against, any and all loss, liability,
damage, claim or expense incurred without negligence or bad faith on its part,
arising out of or in connection with the acceptance or administration of the
trust or trusts hereunder, including the costs and expenses (including
reasonable legal fees and expenses) of defending itself against, or
investigating, any claim or liability in connection with the exercise or
performance of any of its powers or duties hereunder. The obligation to
indemnify as set forth in this Section 8.2 shall survive the termination of this
Series A Capital Securities Guarantee.

                                   ARTICLE IX
                                 MISCELLANEOUS

SECTION 9.1    Successors and Assigns
               ----------------------

          All guarantees and agreements contained in this Series A Capital
Securities Guarantee shall bind the successors, assigns, receivers, trustees
and representatives of the Guarantor and shall inure to the benefit of the
Holders of the Series A Capital Securities then outstanding.

SECTION 9.2    Amendments
               ----------

          Except with respect to any changes that do not materially adversely
affect the rights of Holders (in which case no consent of Holders will be
required), this Series A Capital Securities Guarantee may only be amended with
the prior approval of the Holders of a Majority in liquidation amount of the
Securities (including the stated amount that would be paid on redemption,
liquidation or otherwise, plus accrued and unpaid Distributions to the date
upon which the voting percentages are determined).  The provisions of Section
12.2 of the Declaration with respect to meetings of Holders of the Securities
apply to the giving of such approval.

                                       20
<PAGE>
 
SECTION 9.3    Notices
               -------

          All notices provided for in this Series A Capital Securities Guarantee
shall be in writing, duly signed by the party giving such notice, and shall be
delivered, telecopied or mailed by first class mail, as follows:

          (a) If given to the Issuer, in care of the Administrative Trustee at
the Issuer's mailing address set forth below (or such other address as the
Issuer may give notice of to the Holders):

               First USA Capital Trust I
               c/o First USA, Inc.
               1601 Elm Street
               47th Floor
               Dallas, Texas 75201
               Attention:  Jack M. Antonini

               Telecopy:  (214) 849-2950

          (b) If given to the Capital Securities Guarantee Trustee, at the
Capital Securities Guarantee Trustee's mailing address set forth below (or such
other address as the Capital Securities Guarantee Trustee may give notice of to
the Holders):

               The Bank of New York
               101 Barclay Street, 21 West
               New York, New York 10286
               Attention:  Corporate Trust Trustee
                           Administration
               Telecopy:   (212) 815-5915

          (c) If given to the Guarantor, at the Guarantor's mailing address set
forth below (or such other address as the Guarantor may give notice of to the
Holders):


               First USA, Inc.
               1601 Elm Street
               47th Floor
               Dallas, Texas 75201
               Attention:  Philip E. Taken
               Telecopy:  (214) 849-2068

          (d) If given to any Holder, at the address set forth on the books and
records of the Issuer.

          All such notices shall be deemed to have been given when received in
person, telecopied with receipt confirmed, or mailed by first class mail,
postage prepaid except that if a notice or other document is refused delivery or
cannot be deliv-

                                       21
<PAGE>

 
ered because of a changed address of which no notice was given, such notice or
other document shall be deemed to have been delivered on the date of such
refusal or inability to deliver.

SECTION 9.4    Exchange Offer
               --------------

          In the event an Exchange Offer Registration Statement (as defined in
the Registration Rights Agreement) becomes effective and the Issuer issues any
Series B Capital Securities in the Exchange Offer, the Guarantor will enter into
a new capital securities guarantee agreement, in substantially the same form as
this Series A Capital Securities Guarantee, with respect to the Series B Capital
Securities.

SECTION 9.5    Benefit
               -------

          This Series A Capital Securities Guarantee is solely for the benefit
of the Holders and, subject to Section 3.1(a), is not separately transferable
from the Series A Capital Securities.

SECTION 9.6    Governing Law
               -------------

          THIS SERIES A CAPITAL SECURITIES GUARANTEE SHALL BE GOVERNED BY, AND
CONSTRUED AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK,
WITHOUT REGARD TO CONFLICTS OF LAWS PRINCIPLES THEREOF.

                                       22
<PAGE>
 
          THIS SERIES A CAPITAL SECURITIES GUARANTEE is executed as of the day
and year first above written.

                              FIRST USA, INC. as
                              Guarantor



                              By:/s/ Philip E. Taken
                                 ------------------------
                                 Name:
                                 Title:
 
                              The Bank of New York, as Capital
                              Securities Guarantee Trustee



                              By:/s/ Stephen J. Giurlando
                                 ------------------------
                                 Name:  Stephen J. Giurlando
                                 Title: Assistant Vice President

                                       23