<PAGE>   1
 
                                                                    EXHIBIT 99.1
 
                             LETTER OF TRANSMITTAL
                                      FOR
                           TENDER OF ALL OUTSTANDING
                     9 5/8% SERIES A SENIOR NOTES DUE 2005
                                IN EXCHANGE FOR
                     9 5/8% SERIES B SENIOR NOTES DUE 2005
                                       OF
                         CHESAPEAKE ENERGY CORPORATION
 
                  THE EXCHANGE OFFER WILL EXPIRE AT 5:00 P.M.,
       NEW YORK CITY TIME, ON             , 1998 (THE "EXPIRATION DATE"),
                UNLESS EXTENDED BY CHESAPEAKE ENERGY CORPORATION
 
                 The Exchange Agent for the Exchange Offer is:
 
                    UNITED STATES TRUST COMPANY OF NEW YORK
 
<TABLE>
<CAPTION>
         By Mail:            By Overnight Courier:             By Hand:                By Facsimile:
<S>                        <C>                        <C>                        <C>
 
United States Trust        United States Trust        United States Trust        (212) 420-6152
  Company of New York        Company of New York        Company of New York      (For Eligible Institutions
P.O. Box 844               Corporate Trust Operations 111 Broadway               Only)
Cooper Station               Department               Lower Level
New York, NY 10276-0844    770 Broadway -- 13th Floor New York, NY 10006         Confirm by telephone:
Attention: Corporate Trust New York, NY 10003         Attention: Corporate Trust (800) 548-6565
  Services                                              Services
(registered or certified
mail recommended)
</TABLE>
 
     DELIVERY OF THIS LETTER OF TRANSMITTAL TO AN ADDRESS OTHER THAN AS SET
FORTH ABOVE OR TRANSMISSION OF INSTRUCTIONS VIA A FACSIMILE TRANSMISSION TO A
NUMBER OTHER THAN AS SET FORTH ABOVE WILL NOT CONSTITUTE A VALID DELIVERY.
 
     The undersigned acknowledges receipt of the Prospectus dated          ,
1998 (the "Prospectus") of Chesapeake Energy Corporation ("Chesapeake") which,
together with this Letter of Transmittal (the "Letter of Transmittal"),
constitutes Chesapeake's offer (the "Exchange Offer") to exchange $1,000 in
principal amount of a new series of 9 5/8% Series B Senior Notes Due 2005 (the
"New Notes") of Chesapeake for each $1,000 in principal amount of outstanding
9 5/8% Series A Senior Notes Due 2005 (the "Old Notes") of Chesapeake. The terms
of the New Notes are identical in all material respects (including principal
amount, interest rate and maturity) to the terms of the Old Notes for which they
may be exchanged pursuant to the Exchange Offer, except that the New Notes will
have been registered under the Securities Act of 1933, as amended, and,
therefore, will not bear legends restricting the transfer thereof.
 
     The Exchange Offer is being made pursuant to the Registration Rights
Agreement dated as of April 22, 1998 (the "Registration Rights Agreement"), and
all Old Notes validly tendered will be accepted for exchange. Any Old Notes not
tendered will remain outstanding and continue to accrue interest, but will not
retain any rights under the Registration Rights Agreement. Holders electing to
have Old Notes exchanged pursuant to the Exchange Offer will be required to
surrender such Old Notes, together with the Letter of Transmittal, to the
Exchange Agent at the address specified herein prior to the close of business on
the Expiration Date. Holders will be entitled to withdraw their election, at any
time prior to 5:00 p.m., New York City time on the Expiration Date, by sending
to the Exchange Agent at the address specified herein a facsimile transmission
or letter setting forth the name of such Holder, the principal amount of Old
Notes delivered for exchange and a statement that such Holder is withdrawing
this election to have such Old Notes exchanged.
<PAGE>   2
 
     The undersigned has checked the appropriate boxes below and signed this
Letter of Transmittal to indicate the action the undersigned desires to take
with respect to the Exchange Offer.
 
     PLEASE READ THE ENTIRE LETTER OF TRANSMITTAL AND THE PROSPECTUS CAREFULLY
BEFORE CHECKING ANY BOX BELOW.
 
     THE INSTRUCTIONS INCLUDED WITH THIS LETTER OF TRANSMITTAL MUST BE FOLLOWED.
QUESTIONS AND REQUESTS FOR ASSISTANCE OR FOR ADDITIONAL COPIES OF THE PROSPECTUS
AND THIS LETTER OF TRANSMITTAL MAY BE DIRECTED TO THE EXCHANGE AGENT.
 
     List below the Old Notes to which this Letter of Transmittal relates. If
the space provided below is inadequate, the Certificate Numbers and Principal
Amounts should be listed on a separate signed schedule affixed hereto.
 
<TABLE>
<S>                                <C>                 <C>                 <C>                 <C>
------------------------------------------------------------------------------------------------------------------
                                        DESCRIPTION OF OLD NOTES TENDERED
------------------------------------------------------------------------------------------------------------------
                                                                                               AGGREGATE PRINCIPAL
                                                            AGGREGATE                            AMOUNT TENDERED
NAME(S) AND ADDRESS(ES)                                 PRINCIPAL AMOUNT        AGGREGATE        IN EXCHANGE FOR
OF REGISTERED HOLDER(S)                CERTIFICATE       REPRESENTED BY     PRINCIPAL AMOUNT    CERTIFICATED NEW
(PLEASE FILL IN)                       NUMBER(S)*           OLD NOTES          TENDERED**           NOTES***
------------------------------------------------------------------------------------------------------------------
 
                                   ------------------------------------------------------------------------
 
                                   ------------------------------------------------------------------------
 
                                   ------------------------------------------------------------------------
                                          TOTAL
------------------------------------------------------------------------------------------------------------------
   * Need not be completed by book-entry holder.
  ** Unless otherwise indicated, the holder will be deemed to have tendered the full aggregate principal amount
     represented by Old Notes. See Instruction 2.
 *** Unless otherwise indicated, the holder will be deemed to have tendered Old Notes in exchange for a beneficial
     interest in one or more fully registered global notes, which will be deposited with, or on behalf of, The
     Depository Trust Company ("DTC") and registered in the name of Cede & Co., its nominee.
------------------------------------------------------------------------------------------------------------------
</TABLE>
 
     Unless the context requires otherwise, the term "Holder" for purposes of
this Letter of Transmittal means any person in whose name Old Notes are
registered or any other person who has obtained a properly completed bond power
from the registered holder.
 
     The undersigned has completed the appropriate boxes above and below and
signed this Letter of Transmittal to indicate the action the undersigned desires
to take with respect to the Exchange Offer.
 
     This Letter of Transmittal is to be used either if certificates of Old
Notes are to be forwarded herewith or if delivery of Old Notes is to be made by
book-entry transfer to an account maintained by the Exchange Agent at DTC,
pursuant to the procedures set forth in "The Exchange Offer -- Terms of the
Exchange Offer -- Procedures for Tendering Old Notes" in the Prospectus.
Delivery of this Letter of Transmittal and any other required documents should
be made to the Exchange Agent. Delivery of documents to a book-entry transfer
facility does not constitute delivery to the Exchange Agent.
 
     Holders whose Old Notes are not immediately available or who cannot deliver
their Old Notes and all other documents required hereby to the Exchange Agent on
or prior to the Expiration Date must tender their Old Notes according to the
guaranteed delivery procedure set forth in the Prospectus under the caption "The
Exchange Offer -- Terms of the Exchange Offer -- Procedures for Tendering Old
Notes." See Instruction 1. Holders of Old Notes that are tendering by book-entry
transfer to the Exchange Agent's account at DTC can execute the tender through
the DTC Automated Tender Offer Program ("ATOP") for which the transaction
<PAGE>   3
 
will be eligible. DTC participants should transmit their acceptance to DTC,
which will verify the acceptance and execute a book-entry delivery to the
Exchange Agent's account at DTC. DTC will then send an Agent's Message (as
defined in the Prospectus) to the Exchange Agent for its acceptance. DTC
participants may also accept the Exchange Offer by submitting a notice of
guaranteed delivery through ATOP.
 
[ ]  CHECK HERE IF TENDERED OLD NOTES ARE BEING DELIVERED TO THE EXCHANGE
     AGENT IN EXCHANGE FOR CERTIFICATED NEW NOTES.
 
     Unless the undersigned (i) has provided information in the last column of
the table above entitled "Description of Old Notes Tendered" and (ii) has
checked the box above, the undersigned will be deemed to have tendered Old Notes
in exchange for a beneficial interest in one or more fully registered global
certificates, which will be deposited with, or on behalf of, DTC and registered
in the name of Cede & Co., its nominee. Beneficial interests in such registered
global certificates will be shown on, and transfers thereof will be effected
only through, records maintained by DTC and its participants. See "Description
of Senior Notes -- Book-Entry; Delivery; Form and Transfer" as set forth in the
Prospectus.
 
[ ]  CHECK HERE IF TENDERED OLD NOTES ARE BEING DELIVERED BY BOOK-ENTRY
     TRANSFER MADE TO AN ACCOUNT MAINTAINED BY THE EXCHANGE AGENT WITH A
     BOOK-ENTRY TRANSFER FACILITY AND COMPLETE THE FOLLOWING:
 
Name of Tendering Institution ______________    [ ] The Depository Trust Company
 
Account Number
              ------------------------------------------------------------------
 
Transaction Code Number
                       ---------------------------------------------------------
 
     Holders whose Old Notes are not immediately available or who cannot deliver
their Old Notes and all other documents required hereby to the Exchange Agent on
or prior to the Expiration Date may tender their Old Notes according to the
guaranteed delivery procedure set forth in the Prospectus under the captions
"The Exchange Offer -- Terms of the Exchange Offer -- Procedures for Tendering
Old Notes" and "The Exchange Offer -- Terms of the Exchange Offer -- Guaranteed
Delivery Procedures."
 
[ ]  CHECK HERE IF TENDERED OLD NOTES ARE BEING DELIVERED PURSUANT TO A
     NOTICE OF GUARANTEED DELIVERY AND COMPLETE THE FOLLOWING:
 
Name of Registered Holder(s):
                             ---------------------------------------------------
 
Name of Eligible Institution that Guaranteed Delivery:
                                                      --------------------------
 
Window Ticket Number (if any):
                              --------------------------------------------------
 
Date of Execution of Notice of Guaranteed Delivery:
                                                   -----------------------------
 
If delivered by book-entry transfer:
 
<TABLE>
<S>                <C>                                    <C>
                   Account Number __________              Transaction Code Number __________
</TABLE>
 
              PLEASE READ THE ACCOMPANYING INSTRUCTIONS CAREFULLY
 
Ladies and Gentlemen:
 
     Upon the terms and subject to the conditions of the Exchange Offer, the
undersigned hereby tenders to Chesapeake the above-described principal amount of
Old Notes. Subject to, and effective upon, the acceptance for exchange of the
Old Notes tendered herewith, the undersigned hereby exchanges, assigns and
transfers to, or upon the order of, Chesapeake all right, title and interest in
and to such Old Notes. The undersigned hereby irrevocably constitutes and
appoints the Exchange Agent as the true and lawful agent and attorney-in-fact of
the undersigned (with full knowledge that said Exchange Agent acts as the agent
of the undersigned in connection with the Exchange Offer) to cause the Old Notes
to be assigned, transferred and exchanged. The undersigned represents and
warrants that it has full power and authority to tender, exchange, assign and
transfer the Old Notes and to acquire New Notes issuable upon the exchange of
such tendered Old
<PAGE>   4
 
Notes, and that, when the same are accepted for exchange, Chesapeake will
acquire good and unencumbered title to the tendered Old Notes, free and clear of
all liens, restrictions, charges and encumbrances and not subject to any adverse
claim. The undersigned also warrants that it will, upon request, execute and
deliver any additional documents deemed by Chesapeake to be necessary or
desirable to complete the exchange, assignment and transfer of tendered Old
Notes or to transfer ownership of such Old Notes on the account books maintained
by DTC.
 
     The Exchange Offer is subject to certain conditions as set forth in the
Prospectus under the caption "The Exchange Offer -- Conditions of the Exchange
Offer." The undersigned recognizes that as a result of these conditions (which
may be waived, in whole or in part, by Chesapeake) as more particularly set
forth in the Prospectus, Chesapeake may not be required to exchange any of the
Old Notes tendered hereby and, in such event, the Old Notes not exchanged will
be returned to the undersigned at the address shown below the signature of the
undersigned.
 
     By tendering, each Holder of Old Notes represents to Chesapeake that (i)
the New Notes acquired pursuant to the Exchange Offer are being obtained in the
ordinary course of business of the person receiving such New Notes, whether or
not such person is such Holder, (ii) neither the Holder of Old Notes nor any
such other person has an arrangement or understanding with any person to
participate in the distribution of such New Notes, (iii) if the Holder is not a
broker-dealer or is a broker-dealer but will not receive New Notes for its own
account in exchange for Old Notes, neither the Holder nor any such other person
is engaged in or intends to participate in a distribution of the New Notes and
(iv) neither the Holder nor any such other person is an "affiliate" of
Chesapeake within the meaning of Rule 405 under the Securities Act of 1933, as
amended (the "Securities Act"), or, if such Holder is an "affiliate," that such
Holder will comply with the registration and prospectus delivery requirements of
the Securities Act to the extent applicable.
 
     If the tendering Holder is a broker-dealer (whether or not it is also an
"affiliate" of Chesapeake within the meaning of Rule 405 under the Securities
Act) that will receive New Notes for its own account in exchange for Old Notes
acquired as a result of market-making or other trading activities (other than
Old Notes acquired directly from Chesapeake, or an affiliate of Chesapeake), it
acknowledges that it will deliver a prospectus meeting the requirements of the
Securities Act in connection with any resale of such New Notes and will promptly
notify Chesapeake when it has disposed of all such New Notes. By acknowledging
that it will deliver and by delivering a prospectus meeting the requirements of
the Securities Act in connection with any resale of such New Notes, the
undersigned is not deemed to admit that it is an "underwriter' within the
meaning of the Securities Act.
 
[ ]  CHECK HERE IF YOU ARE A BROKER-DEALER SUBJECT TO A PROSPECTUS DELIVERY
     REQUIREMENT, AND
 
[ ]  CHECK HERE IF YOU WISH TO RECEIVE 10 ADDITIONAL COPIES OF THE PROSPECTUS
     AND 10 COPIES OF ANY AMENDMENTS OR SUPPLEMENTS THERETO
 
    Broker-Dealer Name:
                       ---------------------------------------------------------
 
    Address:
            --------------------------------------------------------------------
 
     Each Holder, by tendering, also acknowledges and agrees that any Holder
using the Exchange Offer to participate in a distribution of the New Notes to be
acquired in the Exchange offer (a) could not rely on the position of the
Commission enunciated in Morgan Stanley and Co., Inc. (available June 5, 1991)
and Exxon Capital Holdings Corporation (available May 13, 1988), as interpreted
in the Commission's letter to Shearman & Sterling (available July 2, 1993), and
similar no-action letters, and (b) must comply with the registration and
prospectus delivery requirements of the Securities Act in connection with a
secondary resale transaction and that such a secondary resale transaction should
be covered by an effective registration statement containing the selling
security holder information required by Item 507 or 508, as applicable, of
Regulation S-K if the resales are of New Notes obtained by such holder in
exchange for Old Notes acquired by such Holder directly from Chesapeake.
<PAGE>   5
 
     All authority herein conferred or agreed to be conferred shall survive the
death, bankruptcy or incapacity of the undersigned and every obligation of the
undersigned hereunder shall be binding upon the heirs, personal representatives,
executors, administrators, successors, assigns, trustees in bankruptcy and other
legal representatives of the undersigned. Tendered Old Notes may be withdrawn at
any time prior to 5:00 p.m., New York City Time on the Expiration Date.
 
     Certificates for all New Notes delivered in exchange for tendered Old Notes
and any Old Notes delivered herewith but not exchanged, in each case registered
in the name of the undersigned, shall be delivered to the undersigned at the
address shown below the signature of the undersigned.
 
     The undersigned recognizes that unless the holder of Old Notes (i) provides
information in the last column of the table above entitled "Description of Old
Notes Tendered" and (ii) checks the box entitled "Check here if tendered shares
of Old Notes are being delivered to the Exchange Agent in exchange for
certificated New Notes" above, such holder, when tendering such Old Notes, will
be deemed to have tendered such Old Notes in exchange for a beneficial interest
in one or more fully registered global certificates, which will be deposited
with, or on behalf of, DTC and registered in the name of Cede & Co., its
nominee. Beneficial interests in such registered global certificates will be
shown on, and transfers thereof will be effected only through, records
maintained by DTC and its participants. See, "Description of Senior
Notes -- Book-Entry; Delivery; Form and Transfer" in the Prospectus.
 
                         TENDERING HOLDER(S) SIGN HERE
 
--------------------------------------------------------------------------------
                           Signature(s) of Holder(s)
 
Date:          , 1998
 
     (Must be signed by registered Holder(s) exactly as name(s) appear(s) on
certificate(s) for Old Notes or by any person(s) authorized to become registered
Holder(s) by endorsements and documents transmitted herewith. If signature by a
trustee, executor, administrator, guardian, attorney-in-fact, officer of a
corporation or other person acting in a fiduciary or representative capacity,
please set forth the full title of such person.) See Instruction 3.
 
Name(s):
        ------------------------------------------------------------------------
 
--------------------------------------------------------------------------------
                                 (Please Print)
 
Capacity (full title):
                      ----------------------------------------------------------
 
Address:
        ------------------------------------------------------------------------
 
--------------------------------------------------------------------------------
                              (Including Zip Code)
 
Area Code and Telephone No.:
                            ----------------------------------------------------
 
Tax Identification No.:
                       ---------------------------------------------------------
<PAGE>   6
 
                           GUARANTEE OF SIGNATURE(S)
                       (IF REQUIRED -- SEE INSTRUCTION 3)
 
Authorized Signature:
                     -----------------------------------------------------------
 
Name:
     ---------------------------------------------------------------------------
 
Title:
      --------------------------------------------------------------------------
 
Address:
        ------------------------------------------------------------------------
 
Name of Firm:
             -------------------------------------------------------------------
 
Area Code and Telephone No.:
                            ----------------------------------------------------
 
Dated:
      ------------------------------, 1998
 
<TABLE>
<S>                                <C>                                           <C>
----------------------------------------------------------------------------------------------------------------------
PAYOR'S NAME: CHESAPEAKE ENERGY CORPORATION
----------------------------------------------------------------------------------------------------------------------
  SUBSTITUTE                       Name (If joint names, list first and circle the name of the person or entity whose
                                   number you enter in Part I below.)
  FORM W-9                         ---------------------------------------------------------------------------------
  Department of the Treasury       Address
  Internal Revenue Service         ---------------------------------------------------------------------------------
                                   City, state and Zip Code
  PAYOR'S REQUEST FOR TAXPAYER     ---------------------------------------------------------------------------------
  IDENTIFICATION NUMBER ("TIN")
  AND CERTIFICATION
                                    PART I -- PLEASE PROVIDE YOUR TAXPAYER       Social Security number or
                                    IDENTIFICATION NUMBER ("TIN") IN THE BOX AT  Employer Identification Number
                                    RIGHT AND CERTIFY BY SIGNING AND DATING
                                    BELOW
 
                                   ---------------------------------------------------------------------------------
                                    PART II -- If exempt from backup withholding, check the box to the right.
                                    Also provide your TIN in Part I and sign and date this form in Part III.     [ ]
                                   ---------------------------------------------------------------------------------
                                    PART III -- Under penalties of perjury, I certify that:
                                    1. The number shown on this form is my correct taxpayer identification number (or
                                       I am waiting for a number to be issued to me), AND
                                    2. I am not subject to backup withholding: (A) I am exempt from backup
                                       withholding; or (B) I have not been notified by the Internal Revenue Service
                                       that I am subject to backup withholding as a result of a failure to report all
                                       interest or dividends, or (C) the IRS has notified me that I am no longer
                                       subject to backup withholding.
                                    CERTIFICATION INSTRUCTIONS. You must cross out item 2 above if you have been
                                    notified by the IRS that you are currently subject to backup withholding because
                                    of underreporting interest or dividends on your tax return.
                                    Signature                                         Date
                                              -------------------------------------       -------------------------
----------------------------------------------------------------------------------------------------------------------
</TABLE>
 
NOTE: FAILURE TO COMPLETE AND RETURN THIS FORM MAY RESULT IN BACKUP WITHHOLDING
      OF 31% OF ANY PAYMENTS MADE TO YOU PURSUANT TO THE EXCHANGE OFFER. PLEASE
      REVIEW THE ENCLOSED GUIDELINES FOR CERTIFICATION OF TAXPAYER
      IDENTIFICATION NUMBER ON SUBSTITUTE FORM W-9 FOR ADDITIONAL DETAILS.
<PAGE>   7
 
                                  INSTRUCTIONS
 
                    FORMING PART OF THE TERMS AND CONDITIONS
                             OF THE EXCHANGE OFFER
 
     1. DELIVERY OF THIS LETTER OF TRANSMITTAL AND CERTIFICATES; GUARANTEED
DELIVERY PROCEDURE. The Letter of Transmittal is to be used to forward, and must
accompany, all certificates representing Old Notes tendered pursuant to the
Exchange Offer. Certificates representing the Old Notes in proper form for
transfer (or a confirmation of book-entry transfer of such Old Notes in the
Exchange Agent's account at the book-entry transfer facility), as well as a
properly completed and duly executed copy of this Letter of Transmittal and all
other documents required by this Letter of Transmittal, must be received by the
Exchange Agent at its address set forth herein prior to 5:00 p.m., New York City
time, on the Expiration Date.
 
     THE METHOD OF DELIVERY OF OLD NOTES, THIS LETTER OF TRANSMITTAL AND ALL
OTHER REQUIRED DOCUMENTS TO THE EXCHANGE AGENT IS AT THE ELECTION AND RISK OF
THE HOLDER AND, EXCEPT AS OTHERWISE PROVIDED BELOW, THE DELIVERY WILL BE DEEMED
MADE ONLY WHEN ACTUALLY RECEIVED OR CONFIRMED BY THE EXCHANGE AGENT. INSTEAD OF
DELIVERY BY MAIL, IT IS RECOMMENDED THAT HOLDERS USE AN OVERNIGHT OR HAND
DELIVERY SERVICE.
 
     Holders whose Old Notes are not immediately available or who cannot deliver
their Old Notes (or a confirmation of book-entry transfer of Old Notes into the
Exchange Agent's account at the book-entry facility) and all other required
documents to the Exchange Agent on or prior to the Expiration Date may tender
their Old Notes pursuant to the guaranteed delivery procedure set forth in the
Prospectus under "The Exchange Offer -- Terms of the Exchange
Offer -- Guaranteed Delivery Procedures." Pursuant to such procedure: (i) such
tender must be made by or through an Eligible Institution (as defined in the
Prospectus); (ii) on or prior to the Expiration Date, the Exchange Agent must
have received from such Eligible Institution a letter, telegram or facsimile
transmission substantially in the form of the Notice of Guaranteed Delivery
available from the Exchange Agent, or an Agent's Message with respect to
guaranteed delivery that is accepted by the Exchange Agent, setting forth the
name and address of the tendering Holder, the name(s) in which such Old Notes
are registered, the principal amount being tendered and (if available) the
certificate number(s) of the Old Notes to be tendered; and (iii) all tendered
Old Notes (or a confirmation of book-entry transfer of such Old Notes into the
Agent's account at DTC) as well as this Letter of Transmittal and all other
documents required by this Letter of Transmittal must be received by the
Exchange Agent within three New York Stock Exchange trading days after the date
of execution of such letter, telegram or facsimile transmission, all as provided
in the Prospectus under the caption "The Exchange Offer -- Terms of the Exchange
Offer -- Guaranteed Delivery Procedures."
 
     A tender will be deemed to have been received as of the date when the
tendering Holder's duly signed Letter of Transmittal accompanied by Old Notes
(or a timely confirmation of a book-entry transfer of Old Notes into the
Exchange Agent's account at the book-entry transfer facility) or a Notice of
Guaranteed Delivery from an Eligible Institution is received by the Exchange
Agent.
 
     No alternative, conditional, irregular or contingent tenders will be
accepted. All tendering Holders, by execution of this Letter of Transmittal (or
facsimile thereof), shall waive any right to receive notice of the acceptance of
the Old Notes for exchange.
 
     2. PARTIAL TENDERS; WITHDRAWALS. Tenders of Old Notes will be accepted in
denominations of $1,000 and integral multiples in excess thereof. If less than
the entire principal amount of Old Notes evidenced by a submitted certificate is
tendered, the tendering Holder must fill in the principal amount tendered in the
column entitled "Aggregate Principal Amount Tendered." A newly issued
certificate for the principal amount of Old Notes submitted but not tendered
will be sent to such Holder as soon as practicable after the Expiration Date.
All Old Notes delivered to the Exchange Agent will be deemed to have been
tendered unless otherwise indicated. To withdraw a tender of Old Notes in the
Exchange Offer, a written or facsimile transmission notice of withdrawal must be
received by the Exchange Agent at its address set forth herein prior to 5:00
p.m., New York City time, on the Expiration Date. Any such notice of withdrawal
must (i) specify the name of the person having deposited the Old Notes to be
withdrawn (the "Depositor"), (ii) identify the Old Notes to be withdrawn
(including the certificate number or numbers and principal amount of such Old
Notes),
<PAGE>   8
 
(iii) contain a statement that such holder is withdrawing its election to have
such Old Notes exchanged, (iv) be signed by the Holder in the same manner as the
original signature on the Letter of Transmittal by which such Old Notes were
tendered (including any required signature guarantees) or be accompanied by
documents of transfer sufficient to have the Trustee with respect to the Old
Notes register the transfer of such Old Notes in the name of the person
withdrawing the tender and (v) specify the name in which any such Old Notes are
to be registered, if different from that of the Depositor. If Old Notes have
been tendered pursuant to the procedure for book-entry transfer, any notice of
withdrawal must specify the name and number of the account at the book-entry
transfer facility from which the Old Notes were tendered, identify the principal
amount of tendered Old Notes to be withdrawn, and specify the name and number of
the account at the book-entry transfer facility to be credited with the
withdrawn Old Notes and otherwise comply with DTC's procedures. All questions as
to the validity, form and eligibility (including time of receipt) of such
notices will be determined by Chesapeake, whose determination shall be final and
binding on all parties. Any Old Notes so withdrawn will be deemed not to have
been validly tendered for purposes of the Exchange Offer and no New Notes will
be issued with respect thereto unless the Old Notes so withdrawn are validly
retendered. Any Old Notes which have been tendered but which are not accepted
for exchange will be returned to the Holder thereof without cost to such Holder
as soon as practicable after withdrawal, rejection of tender or termination of
the Exchange Offer. Properly withdrawn Old Notes may be retendered by following
one of the procedures described herein at any time prior to the business day
prior to the Expiration Date.
 
     3. SIGNATURE ON THIS LETTER OF TRANSMITTAL; WRITTEN INSTRUMENTS AND
ENDORSEMENTS; GUARANTEE OF SIGNATURES. If this Letter of Transmittal is signed
by the registered Holder(s) of the Old Notes tendered hereby, the signature must
correspond with the name(s) as written on the face of certificates without
alteration, enlargement or any change whatsoever.
 
     If tendered Old Notes are registered in the name of the signer of the
Letter of Transmittal and the New Notes to be issued in exchange therefor are to
be issued (and any untendered Old Notes are to be reissued) in the name of the
registered holder (including any participant in The Depository Trust Company
(also referred to as a book-entry facility) whose name appears on a security
listing as the owner of Old Notes), the signature of such signer need not be
guaranteed. In any other case, the tendered Old Notes must be endorsed or
accompanied by written instruments of transfer in form satisfactory to
Chesapeake and duly executed by the registered holder and the signature on the
endorsement or instrument of transfer must be guaranteed by an eligible
guarantor institution which is a member of one of the following recognized
signature guarantee programs (an "Eligible Institution"): (i) The Securities
Transfer Agents Medallion Program (STAMP), (ii) The New York Stock Exchange
Medallion Signature Program (MSF), or (iii) The Stock Exchange Medallion Program
(SEMP).
 
     If the New Notes or Old Notes not exchanged are to be delivered to an
address other than that of the registered holder appearing on the note register
for the Old Notes, the signature in the Letter of Transmittal must be guaranteed
by an Eligible Institution.
 
     Endorsements on certificates or signatures on separate written instruments
of transfer or exchange required by this Instruction 3 must be guaranteed by an
Eligible Institution.
 
     If any of the Old Notes tendered hereby are owned of record by two or more
joint owners, all such owners must sign this Letter of Transmittal.
 
     If a number of Old Notes registered in different names are tendered, it
will be necessary to complete, sign and submit as many separate copies of this
Letter of Transmittal as there are different registrations of Old Notes.
 
     When this Letter of Transmittal is signed by the registered Holder or
Holders of Old Notes listed and tendered hereby, no endorsements of certificates
or separate written instruments of transfer or exchange are required.
 
     If this Letter of Transmittal is signed by a person other than the
registered Holder or Holders of the Old Notes listed, such Old Notes must be
endorsed or accompanied by separate written instruments of transfer or
<PAGE>   9
 
exchange in form satisfactory to Chesapeake and duly executed by the registered
Holder or Holders, in either case signed exactly as the name or names of the
registered Holder or Holders appear(s) on the Old Notes.
 
     If this Letter of Transmittal, any certificates or separate written
instruments of transfer or exchange are signed by trustees, executors,
administrators, guardians, attorneys-in-fact, officers of corporations or others
acting in a fiduciary or representative capacity, such persons should so
indicate when signing, and, unless waived by Chesapeake, proper evidence
satisfactory to Chesapeake of their authority so to act must be submitted.
 
     4. TRANSFER TAXES. Chesapeake shall pay all transfer taxes, if any,
applicable to the exchange of Old Notes pursuant to the Exchange Offer. If,
however, certificates representing New Notes, or Old Notes for principal amounts
not tendered or accepted for exchange, are to be delivered to, or are to be
issued in the name of, any person other than the registered Holder of the Old
Notes tendered hereby, or if a transfer tax is imposed for any reason other than
the exchange of Old Notes pursuant to the Exchange Offer, then the amount of any
such transfer taxes (whether imposed on the registered Holder or any other
person) will be payable by the tendering Holder. If satisfactory evidence of
payment of such taxes or exemption therefrom is not submitted herewith, the
amount of such transfer taxes will be billed directly to such tendering Holder.
 
     Except as provided in this Instruction 4, it will not be necessary for
transfer tax stamps to be affixed to the Old Notes listed in this Letter of
Transmittal.
 
     5. WAIVER OF CONDITIONS. Chesapeake reserves the absolute right to waive,
in whole or in part, any of the conditions to the Exchange Offer set forth in
the Prospectus.
 
     6. MUTILATED, LOST, STOLEN OR DESTROYED NOTES. Any Holder whose Old Notes
have been mutilated, lost, stolen or destroyed should contact the Exchange Agent
at the address indicated above for further instructions.
 
     7. REQUESTS FOR ASSISTANCE OR ADDITIONAL COPIES. Questions relating to the
procedure for tendering and other questions relating to the Exchange Offer, as
well as requests for assistance or additional copies of the Prospectus and this
Letter of Transmittal, may be directed to the Exchange Agent at the address and
telephone number set forth above and in the Prospectus.
 
     8. IRREGULARITIES. All questions as to the validity, form, eligibility
(including time of receipt), and acceptance of Letters of Transmittal or Old
Notes will be resolved by Chesapeake, whose determination will be final and
binding. Chesapeake reserves the absolute right to reject any or all Letters of
Transmittal or tenders that are not in proper form or the acceptance of which
would, in the opinion of Chesapeake's counsel, be unlawful. Chesapeake also
reserves the right to waive any irregularities or conditions of tender as to the
particular Old Notes covered by any Letter of Transmittal or tendered pursuant
to such Letter of Transmittal. None of Chesapeake, the Exchange Agent or any
other person will be under any duty to give notification of any defects or
irregularities in tenders or incur any liability for failure to give any such
notification. Chesapeake's interpretation of the terms and conditions of the
Exchange Offer shall be final and binding.
 
     9. DEFINITIONS. Capitalized terms used in this Letter of Transmittal and
not otherwise defined have the meanings given in the Prospectus.
 
     10. TAX IDENTIFICATION NUMBER. Federal income tax law requires that a
holder of any Old Notes which are accepted for exchange must provide Chesapeake
(as payor) with its correct taxpayer identification number ("TIN"), which, in
the case of a holder who is an individual, is his or her social security number.
If Chesapeake is not provided with the correct TIN, the holder may be subject to
a $50 penalty imposed by the Internal Revenue Service. (If withholding results
in an over-payment of taxes, a refund may be obtained.) Certain holders
(including, among others, all corporations and certain foreign individuals) are
not subject to these backup withholding and reporting requirements; however,
these holders still must submit the Substitute Form W-9. See the enclosed
"Guidelines for Certification of Taxpayer Identification Number on Substitute
Form W-9" for additional instructions.
 
     To prevent backup withholding, each tendering holder must provide such
holder's correct TIN by completing the Substitute Form W-9 set forth herein,
certifying that the TIN provided is correct (or that such
<PAGE>   10
 
holder is awaiting a TIN), and that (i) the holder has not been notified by the
Internal Revenue Service that such holder is subject to backup withholding as a
result of failure to report all interest or dividends or (ii) the Internal
Revenue Service has notified the holder that such holder is no longer subject to
backup withholding. The Form must be signed, even if the holder is exempt from
backup withholding. If the Old Notes are registered in more than one name or are
not in the name of the actual owner, consult the enclosed "Guidelines for
Certification of Taxpayer Identification Number on Substitute Form W-9" for
information on which TIN to report.
 
     Chesapeake reserves the right in its sole discretion to take whatever steps
are necessary to comply with its obligation regarding backup withholding.
 
     IMPORTANT: THIS LETTER OF TRANSMITTAL OR A FACSIMILE THEREOF (TOGETHER WITH
CERTIFICATES FOR OLD NOTES AND ALL OTHER REQUIRED DOCUMENTS) OR A NOTICE OF
GUARANTEED DELIVERY MUST BE RECEIVED BY THE EXCHANGE AGENT ON OR PRIOR TO THE
EXPIRATION DATE.