<PAGE>
 
                                                                   EXHIBIT 10.35

                   -----------------------------------------





                              PURCHASE AGREEMENT

                                     AMONG

                   -----------------------------------------

                              PJ AMERICA, INC.,

                        OHIO PIZZA DELIVERY CO., INC.,

                                 PJ UTAH, LLC,

                                      AND

                                    MEMBERS
                                        



                               September 3, 1998          
<PAGE>

                               TABLE OF CONTENTS

            

Section                                                                    Page 

1.  Purchase and Sale of Company interests; Effective Date..................  1
    1.1  Purchase and Sale..................................................  1
    1.2  Effective Date.....................................................  1

2.  Purchase Price; Payment; 754 Election...................................  1
    2.1  Purchase Price.....................................................  1
    2.2  Payment of Purchase Price..........................................  1
    2.3  754 Election.......................................................  2

3.  Certain Representations and Warranties of Members.......................  2
    3.1  Title to Shares; Share Restrictions................................  2
    3.2  Authority..........................................................  2
    3.3  No Other Interests.................................................  2
    3.4  No Encumbrances On Assets or Properties of Company.................  2
    3.5  Company Distributions and Compensation.............................  2

4.  Representations and Warranties of Buyers................................  2
    4.1  Authorization......................................................  3
    4.2  No Other Representations and Warranties by Members.................  3

5.  Covenants of the Parties................................................  3
    5.1  Payment of Development Debt........................................  3
    5.2  Release of Other Guarantees........................................  3
    5.3  Mutual Release.....................................................  3
    5.4  Indemnity by the Members...........................................  3
    5.5  Indemnity by Buyers................................................  4
    5.6  Limitations on Members' Indemnification Obligations................  4
    5.7  Preparation of Tax Returns.........................................  4

6.  Miscellaneous Provisions................................................  4
    6.1  Expenses...........................................................  4
    6.2  Notice.............................................................  4
    6.3  Exhibits; Entire Agreement.........................................  5
    6.4  Amendment; Waiver..................................................  5
    6.5  Binding Effect; Assignment.........................................  6
    6.6  Captions...........................................................  6
    6.7  Severability of Provisions.........................................  6
    6.8  Governing Law......................................................  6


                                       -i-                           
<PAGE>
                              TABLE OF CONTENTS 
 
Section                                                                    Page
 
  6.9   Publicity; No Disclosure.........................................     6
  6.10  Post-Closing Access..............................................     6
  6.11  Counterparts.....................................................     6


                                     -ii- 
<PAGE>
 
                                   EXHIBITS

Description                                                             Exhibit

Purchase Price Payments...............................................        A


                                     -iii-
<PAGE>
 
                              PURCHASE AGREEMENT

     This Purchase Agreement ("Agreement") is entered into as of September 3,
1998, by and among (i) PJ America, Inc., a Delaware corporation ("PJAM"), (ii)
Ohio Pizza Delivery Co., Inc., an Ohio corporation ("OPD"), (iii) PJ Utah, LLC,
a Utah limited liability company ("Company"), and (iv) the Members of the
Company identified on the signature pages hereto (individually, a "Member" and
collectively, the "Members").


     Recitals:

     A.  The Company owns, operates and manages restaurants as a franchisee of
Papa John's International Inc. ("PJI"). The Members own all of the issued and
outstanding membership interests of the Company ("Company Interests").

     B.  PJAM and OPD (collectively, "Buyers") desire to purchase from the
Members, and the Members desire to sell to Buyers, for the consideration and
pursuant to the terms, conditions and covenants of this Agreement, all of the
Company Interests.


     Agreement:

     Now, Therefore, the parties hereby agree as follows:

1.   Purchase and Sale of Company interests; Effective Date.

     1.1  Purchase and Sale.  Upon the terms set forth herein, (i) PJAM hereby
purchases and acquires 20% of all Company Interests held by each Member, (ii)
OPD hereby purchases and acquires 80% of all Company Interests held by each
Member, and (iii) each Member hereby sells, transfers, conveys, assigns and
delivers to Buyers, all the Company Interests owned by such Member.

     1.2  Effective Date.  Pursuant to an agreement of the parties dated August
24, 1998, the Closing of the purchase and sale of the Company Interests shall,
for all purposes, be effective as of 12:01 A.M., local time, on August 24, 1998.

2.   Purchase Price; Payment; 754 Election.

     2.1  Purchase Price.  The aggregate purchase price ("Purchase Price") for
all of the Company Interests is $815,002.00.

     2.2  Payment of Purchase Price.  Simultaneously with the execution hereof,
the Purchase Price has been paid to the Members in those amounts set forth on
Exhibit A attached hereto, by delivery of immediately available funds to an
account designated by each Member.  Each Member hereby acknowledges the receipt
and sufficiency of the amount of the Purchase Price paid to such Member as set
forth in Exhibit A.                                           
<PAGE>
 
     2.3  754 Election.  In connection with the transfer of Company Interests
hereunder, the parties agree to make such elections permitted under Section 754
of the Internal Revenue Code of 1986, as amended (the "Code") so as to cause the
basis of the Company's property to be adjusted, pursuant to section 743(b) of
the Code.

3.   Certain Representations and Warranties of Members. Each of the Members 
hereby severally represents and warrants to Buyers as follows:

     3.1  Title to Shares; Share Restrictions.  The Member is the sole record,
lawful and beneficial owner of the Company Interests conveyed by such Member to
Buyers hereby and has good and marketable title to such Company Interests. The
Member owns such Company Interests free and clear of all "Encumbrances" (which,
as used in this Agreement, shall mean any charge, claim, community property
interest, condition, equitable interest, lien, mortgage, easement, servitude,
right-of-way, option, pledge, security interest, right of first refusal or
restriction of any kind, including any restriction on use, voting, transfer,
receipt of income or exercise of any other attribute of ownership), other than
restrictions on transfer under applicable state and federal securities laws, and
any restrictions under any shareholder or similar agreement among the Members
and the Company, or any of them, which each Member agrees are hereby waived.

     3.2  Authority.  The Member has full right, power, authority and capacity
to execute, deliver and perform this Agreement in accordance with its terms.
This Agreement constitutes the valid and legally binding obligation of the
Member, enforceable against the Member in accordance with its terms.

     3.3  No Other Interests.  The Company Interests conveyed by such Member to
Buyers hereby constitutes such Member's sole and complete interest in the
Company. Such Member has never conveyed any portion of such Member's membership
interest in the Company. To the knowledge of each Member, the Members constitute
the only persons or entities holding or having any right to Company Interests.

     3.4  No Encumbrances On Assets or Properties of Company.  Such Member has
not subjected any of the assets or properties of the Company to any Encumbrance,
except in the case of Douglas S. Stephens ("Stephens"), D. Ross Davison
("Davison") and Dwayne Hunt in connection with their management of the Company
for PJAM.

     3.5  Company Distributions and Compensation.  Each Member acknowledges that
he is entitled to no further distributions or compensation from the Company in
his capacity as a Member or in any other capacity, except that Stephens and
Davison may be entitled to compensation for services rendered to the Company in
their status as employees of the Company following the date hereof.

4.   Representations and Warranties of Buyers.  Each Buyer represents and
warrants to the Company and the Members as follows:
<PAGE>
 
     4.1  Authorization.  This Agreement has been duly executed and delivered by
such Buyer and constitutes its legal, valid and binding obligation, enforceable
in accordance with the terms of this Agreement. Such Buyer has full power and
authority, corporate and otherwise, to enter into and to deliver this Agreement
and perform the transactions described herein.

     4.2  No Other Representations and Warranties by Members.  Each Buyer
acknowledges that, except as expressly set forth in Section 3 hereof, the
Members make no representations and warranties regarding the Company, its
business, its assets or properties. Each Buyer represents and warrants to the
Members that, as a result of PJAM's management of the Company and its business
pursuant to various agreements between PJAM and the Company, each Buyer is
intimately familiar with the Company and its operations and, in fact, has much
more knowledge then do the Members regarding the Company's business, assets and
liabilities.

5.   Covenants of the Parties.

     5.1  Payment of Development Debt.  Buyers acknowledge that the Company is
indebted to PJI in the approximate principal amount of $2,500,000 with respect
to loans and credit extended to the Company by PJI for start-up, instruction and
operating expenses of the Company (the "Development Debt"), and that payment of
the Development Debt is guaranteed by certain of the Members. Promptly upon the
execution hereof, Buyers shall take all necessary steps to cause the Company to
pay to PJI the entire outstanding amount (including accrued and unpaid interest
thereon) of the Development Debt and to release the Members from their guarantee
of the Development Debt.

     5.2  Release of Other Guarantees.  Buyers acknowledge that certain of the
Members have guaranteed the Company's obligations under certain of the Company's
leases and contracts and under certain debt of the Company to PJAM
(collectively, the "Member Guarantees"). Buyers hereby assume and agree to
perform all of the Members' obligations under the Member Guarantees (and release
the Members from their Member Guarantees of the Company's debt to PJAM), and
shall indemnify the Members with respect thereto pursuant to the provisions of
Section 5.5.

     5.3  Mutual Release.  PJAM, OPD, and the Company, on the one hand, and each
of Members, on the other hand, for themselves, and their respective successors,
assigns, heirs and legal and personal representatives, hereby release and
forever discharge the other from all claims, demands, damages, liabilities,
actions, causes of actions, rights, agreements, promises, losses, costs,
expenses and controversies of very kind and description, matured or unmatured,
liquidated or unliquidated, contingent or otherwise, which they now have, may
now have, or may have had or may hereafter have against the other, arising out
of or connected with, directly or indirectly, the Company, its operations,
assets and properties, or in the case of the Members, such Members' status as a
member of the Company; provided, however, that the foregoing release shall not
be deemed to affect any party's rights or obligations under this Agreement, or
any rights to indemnification under the Company's organizational documents.
<PAGE>
 
     5.4  Indemnity by the Members.  Each Member, severally, shall defend and
indemnify Buyers and shall hold Buyers and the Company harmless, from and
against the following:

          (a)  all liabilities, debts, obligations, losses, damages,
deficiencies, penalties, claims, actions, suits, proceedings, investigations,
demands, assessments, orders and judgments (whether fixed, contingent, accrued,
absolute or otherwise) incurred by Buyers or the Company resulting from, arising
out of, or in connection with any misrepresentation or breach of a
representation or warranty of such Member contained in Section 3 (a "Section 3
Indemnity") (which shall be the sole and exclusive obligation of the Member who
has misrepresented or breached the representation or warranty giving rise to the
Section 3 Indemnity, and no other Member and

          (b)  any and all costs and expenses incident to any of the foregoing,
including, but not limited to, reasonable attorneys' and accountants' fees.

     5.5  Indemnity by Buyers.  Buyers shall defend and indemnify the Members
and hold them harmless from and against the following:

          (a)  all liabilities, debts, obligations, losses, damages,
deficiencies, penalties, claims, actions, suits, proceedings, investigations,
demands, assessments, orders and judgments (whether fixed, contingent, accrued,
absolute or otherwise) incurred by the Members resulting from, arising out of,
or in connection with (i) any inaccurate representation or warranty or the
breach of any representation or warranty of Buyers contained in this Agreement,
or (ii) any breach or default in the performance by Buyers of any agreement,
covenant or undertaking which either is to perform under this Agreement; and

          (b)  any and all costs and expenses incident to any of the foregoing,
including, but not limited to, reasonable attorneys' and accountants' fees.

     5.6  Limitations on Members' Indemnification Obligations'.  In no event
shall the aggregate liability of any individual Member for a Section 3 Indemnity
exceed an amount equal to that portion of the Purchase Price paid to such
Member, as set forth in Exhibit A.

     5.7  Preparation of Tax Returns.  Buyers shall cause to be prepared and
deliver to each Member, at Buyers' expense, the Company's federal and applicable
state tax returns (including schedules K-1 for each Member) for the Company's
tax year ending as a result of the transfer of Company Interests to Buyers
pursuant to the provisions hereof.

6.   Miscellaneous Provisions.

     6.1  Expenses.  Except as otherwise expressly provided in this Agreement,
the fees and expenses incurred by Buyers and the Members in connection with the
preparation, execution and performance of this Agreement shall be paid Buyers.

     6.2  Notice.  All notices, requests, demands and other communications
required or permitted to be given or made under this Agreement shall be in
writing and shall be deemed delivered on (a) the date of personal delivery or
facsimile transmission, (b) the first business day after the date
<PAGE>

of delivery to a nationally recognized overnight courier service, or (c) the
third business day after the date of deposit in the United States mail, postage
prepaid, by registered or certified mail, return receipt requested in each case,
addressed as follows, or to such other address, person or entity as either party
shall designate by notice to the other in accordance herewith:

<TABLE>
                      <S>                   <C>  
                      If to PJAM or OPD:    PJ America, Inc.
                                            9109 Parkway East
                                            Birmingham, AL  35206
                                            Attn: D. Ross Davison,
                                            Chief Financial Officer
                                            FAX: (205) 836-0376

                           With copy to:    Scott Dolson
                                            Brown, Todd & Heyburn PLLC
                                            400 West Market Street, 32nd Floor
                                            Louisville, KY 40202-3363
                                            FAX: (502) 581-1087

                    If to the Company or    Douglas S. Stephens
                            the Members:    9109 Parkway East
                                            Birmingham, AL  35206
                                            FAX: (205) 836-0376

                                                       and

                                            Michael M. Fleishman
                                            Greenebaum Doll & McDonald PLLC
                                            3300 National City Tower
                                            Louisville, KY 40202
                                            FAX:  (502) 587-3695

                           With copy to:    Patrick J. Welsh, Esq.
                                            Greenebaum Doll & McDonald, pllc
                                            3300 National City Tower
                                            Louisville, Kentucky 40202-3197
                                            FAX: (502) 587-3695
</TABLE>

     6.3  Exhibits; Entire Agreement.  The Exhibit to this Agreement shall be
deemed to be incorporated herein by reference and made a part hereof as if set
out in full at the place where first mentioned. As used herein the term
"Agreement" shall mean this Stock Purchase Agreement and the Exhibit hereto.
This Agreement embodies the entire agreement and understanding of the parties
hereto regarding its subject matter and supersedes all prior agreements,
correspondence, arrangements and understandings relating to the subject matter
hereof. No representation, promise, inducement or statement of intention has
been made by any party which has not been embodied in this Agreement.
<PAGE>
 
     6.4  Amendment; Waiver.  This Agreement may be amended, modified,
superseded, or canceled only by a written instrument signed by all of the
parties hereto, and any of the terms, provisions, and conditions hereof may be
waived, only by a written instrument signed by the waiving party. Failure of any
party at any time or times to require performance of any provision hereof shall
not be considered to be a waiver of any succeeding breach of such provision by
any party.

     6.5  Binding Effect; Assignment.  All the terms, provisions and conditions
of this Agreement shall be binding upon and shall inure to the benefit of and be
enforceable by the parties hereto and their respective heirs, legal
representatives, successors and assigns.

     6.6  Captions.  The captions in this Agreement are included for purposes of
convenience only and shall not be considered a part of the Agreement in
construing or interpreting any provision hereof.

     6.7  Severability of Provisions.  If any provision of this Agreement or the
application thereof to any person or circumstance shall to any extent be held in
any proceeding to be invalid or unenforceable, the remainder of this Agreement,
or the application of such provision to persons or circumstances other than
those to which it was held to be invalid or unenforceable, shall not be affected
thereby, and shall be valid and be enforceable to the fullest extent permitted
by law, but only if and to the extent such enforcement would not materially and
adversely frustrate the parties' essential objectives as expressed herein.

     6.8  Governing Law.  This Agreement shall be governed by, and shall be
construed and enforced in accordance with, the laws of the State of Delaware.

     6.9  Publicity; No Disclosure.  Before the Closing, no party to this
Agreement shall make any press release or make any other public announcement
regarding the existence of this Agreement or the transactions described in this
Agreement, without prior consultation with and consent of the other parties to
this Agreement, except as may be required to comply with applicable securities
laws or exchange regulations.

     6.10  Post-Closing Access.  Following the Closing, Buyers shall cause the
Company to provide each of the Members reasonable access to the books and
records of the Company related to periods prior to Closing for purposes of
preparing such Shareholder's federal, state and local income tax returns and for
such other purposes as may be reasonably requested by such Shareholder.

     6.11  Counterparts.  This Agreement may be executed in one or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.
<PAGE>
 
     In Witness Whereof, the parties have entered into this Agreement as of the
date first written above.

                                               PJ America, Inc.

 
                                               By:
                                                  ------------------------------
                                               Title:
                                                     ---------------------------
                                                               ("PJAM")


                                               Ohio Pizza Delivery Co., Inc.
 

                                               By:
                                                  ------------------------------
                                               Title:
                                                     ---------------------------
                                                               ("OPD")


                                               PJ Utah, LLC
 

                                               By:
                                                  ------------------------------
                                               Title:
                                                     ---------------------------
                                                             ("Company")


                                               ---------------------------------
                                               Richard F. Sherman


                                               ---------------------------------
                                               Frank O. Keener


                                               ---------------------------------
                                               Stephen P. Langford


                                               ---------------------------------
                                               Douglas S. Stephens


                                               ---------------------------------
                                               Martin H. Hart


                                               ---------------------------------
                                               Jack A. Laughery


<PAGE>

                                               
                                               ---------------------------------
                                               Michael J. Grisanti

                                               
                                               ---------------------------------
                                               Michael M. Fleishman

                                               
                                               ---------------------------------
                                               Dwayne Hunt

                                               
                                               ---------------------------------
                                               James S. Riekel

                                               
                                               ---------------------------------
                                               D. Ross Davison



<PAGE>
 
                                   EXHIBIT A
                                   ---------



<TABLE>
<CAPTION>

--------------------------------------------------------------------------------
       Member                     Type Interest            Purchase Price
================================================================================
<S>                               <C>                      <C>
 Richard F. Sherman                  Class A                 $170,616.00
--------------------------------------------------------------------------------
 Frank O. Keener                     Class A                 $146,554.00
--------------------------------------------------------------------------------
 Stephen P. Langford                 Class A                 $ 80,933.00
--------------------------------------------------------------------------------
 Douglas S. Stephens                 Class A                 $ 80,933.00
--------------------------------------------------------------------------------
 Martin H. Hart                      Class A                 $ 67,809.00
--------------------------------------------------------------------------------
 Jack A. Laughery                    Class A                 $ 89,683.00
--------------------------------------------------------------------------------
 Michael J. Grisanti                 Class A                 $ 67,809.00
--------------------------------------------------------------------------------
 Michael M. Fleishman                Class A                 $100,619.00
--------------------------------------------------------------------------------
 Dwayne Hunt                         Class B                    $1.00
--------------------------------------------------------------------------------
 James S. Riekel                     Class A                 $ 10,044.00
--------------------------------------------------------------------------------
 D. Ross Davison                     Class B                    $1.00
--------------------------------------------------------------------------------
</TABLE>