<PAGE>
 

                                                                        10.10(c)
                                             
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                              TRANCHE C SUPPLEMENT

                                      among

                           EXTENDED STAY AMERICA, INC.

                                       and

                             VARIOUS TRANCHE C BANKS





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

                          Dated as of December 15, 1998

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



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<PAGE>

                                                                          Page 1
 
                              TRANCHE C SUPPLEMENT
                                                    DATED:  December 15, 1998
 

                  Reference is made to the Credit Agreement  described in Item 1
of Annex I annexed  hereto and made a part hereof (as such Credit  Agreement may
hereafter  be  amended,  modified,  extended,  renewed,  replaced,  restated  or
supplemented from time to time, the "Credit Agreement"). Unless defined in Annex
I attached  hereto,  capitalized  terms defined in the Credit Agreement are used
herein  as  therein  defined.  Extended  Stay  America,  Inc.  and  each  of the
undersigned  lending  institutions  (each a  "Tranche C Bank")  hereby  agree as
follows:

                  1. Each Tranche C Bank agrees  that,  subject to the terms and
conditions set forth herein,  in Annex I and in the Credit  Agreement,  it shall
provide the Commitment under the Relevant Tranche C Term Loan  Sub-Facility,  as
is  indicated  for such Tranche C Bank in Item 3 of Annex I. Each Tranche C Bank
hereby  agrees  that after  giving  effect to this  Tranche C  Supplement,  each
Tranche C Bank's Tranche C Term Loan  Commitment  will be as set forth in Item 3
of Annex I  hereto.  As used  herein,  the term  "Relevant  Tranche  C Term Loan
Sub-Facility"  shall  mean the  Tranche  C Term  Loan  Sub-Facility  established
pursuant to the Tranche C Supplement dated December 15, 1998.

                  2. Each  Tranche C Bank (i)  confirms  that it has  received a
copy of the Credit  Agreement  and the other  Credit  Documents,  together  with
copies of the financial  statements referred to therein and such other documents
and information as it has deemed appropriate to make its own credit analysis and
decision  to enter into this  Tranche C  Supplement;  (ii)  agrees that it will,
independently and without reliance upon any Agent or any other Bank and based on
such  documents  and  information  as it shall  deem  appropriate  at the  time,
continue to make its own credit  decisions in taking or not taking  action under
the Credit Agreement; (iii) appoints and authorizes the Administrative Agent and
the  Syndication  Agent to take  such  action as  agents  on its  behalf  and to
exercise such powers under the Credit  Agreement and the other Credit  Documents
as are delegated to the  Administrative  Agent and the Syndication  Agent by the
terms thereof,  together with such powers as are reasonably  incidental thereto;
and (iv) agrees that it will perform in  accordance  with their terms all of the
obligations  which by the  terms of the  Credit  Agreement  are  required  to be
performed  by it as a Bank;  and (v) in the case of a Tranche C Bank that is not
already  a Bank  under the  Credit  Agreement  and which is not a United  States
person (as such term is defined in Section  7701(a)(30) of the Code) for Federal
income tax  purposes,  agrees to provide to the Borrower and the  Administrative
Agent the  appropriate  Internal  Revenue  Service  Forms (and,  if applicable a
Section  4.04(b)(ii)  Certificate)  described  in Section  4.04(b) of the Credit
Agreement.

                  3. Following the execution of this Tranche C Supplement by the
Borrower and the Tranche C Banks, an executed original hereof (together with all
attachments) will be delivered to the Administrative Agent. Upon the delivery of
a  fully  executed  original  hereof  to  the  Administrative  Agent,  as of the
Supplement  Effective  Date,  each Tranche C Bank shall be a party to the Credit
Agreement  and, to the extent  provided in this Tranche C  Supplement,  have the
rights  and  obligations  of a  Bank  thereunder  and  under  the  other  Credit
Documents.
<PAGE>

                                                                          Page 2
 
                  4. This Tranche C Supplement  shall become effective as of the
date (the  "Supplement  Effective  Date") when (i) the Borrower,  each Tranche C
Bank and the Syndication  Agent shall have signed a counterpart  hereof (whether
the same or different  counterparts) and shall have delivered  (including by way
of  telecopier)  the same to the  Administrative  Agent at the Notice Office and
(ii) each  condition  precedent  set forth in Item 9 of Annex I attached  hereto
shall have been satisfied.

                  5.  THIS  TRANCHE  C  SUPPLEMENT  SHALL BE  GOVERNED  BY,  AND
CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

                  6.  From  and  after  the  Supplement   Effective   Date,  all
references in the Credit  Agreement and the other Credit Documents to the Credit
Agreement  shall  be  deemed  to  be  references  to  the  Credit  Agreement  as
supplemented hereby.
<PAGE>

                                                                          Page 3
 
                  IN WITNESS  WHEREOF,  the  parties  hereto  have  caused  this
Tranche C Supplement to be executed by their respective  officers thereunto duly
authorized, as of the date first above written.

                                        EXTENDED STAY AMERICA, INC.
 
                                        By:  /s/  Robert A. Brannon
                                             ----------------------
                                             Name:  Robert A. Brannon
                                             Title: Senior Vice-President

Acknowledged and Agreed:                MORGAN STANLEY SENIOR FUNDING
                                        INC., Individually, as Syndication Agent
MORGAN STANLEY SENIOR                   and as Arranger
FUNDING, INC. as Syndication Agent
and as Arranger                         By:   /s/  Michael T. McLaughlin
                                              --------------------------
                                              Name:  Michael T. McLaughlin
By:  /s/  Michael T. McLaughlin               Title:    Principal


                                        THE INDUSTRIAL BANK OF JAPAN,
                                        LIMITED, Individually and as 
                                        Administrative Agent

                                        By:   /s/  Takuya Honjo
                                              -------------------------
                                              Name:  Takuya Honjo
                                              Title:    Senior Vice President
<PAGE>

                                                                          Page 4
 
                                            KZH STERLING LLC



                                            By:   /s/  Virginia Conway
                                                  ---------------------
                                                  Name:  Virginia Conway
                                                  Title:    Authorized Agent


                                            FRANKLIN FLOATING RATE TRUST


                                            By:   /s/  Chauncey Lufkin
                                                  ---------------------
                                                  Name:  Chauncey Lufkin
                                                  Title:


                                            PILGRIM PRIME RATE TRUST


                                            By:   /s/  Jeffrey A. Bakalar
                                                  -----------------------
                                                  Name:  Jeffrey A. Bakalar
                                                  Title:  Vice President


                                            ARCHIMEDES FUNDING II, LTD.

                                            By:  ING CAPITAL ADVISORS, INC., as
                                                 Collateral Managers

                                            By:   /s/  Michael J. Campbell
                                                  ------------------------
                                                  Name:  Michael J. Campbell
                                                 Title:  Senior Vice President
                                                          & Portfolio Manager


                                            KZH ING-3 LLC


                                            By: /s/  Virginia Conway
                                                --------------------
                                                Name:  Virginia Conway
                                                Title:    Authorized Agent
<PAGE>


                                                                          Page 5
                                             KZH ING-1 LLC



                                             By: /s/  Virginia Conway
                                                 --------------------
                                                 Name:  Virginia Conway
                                                 Title:    Authorized Agent
<PAGE>
 
                                                                    ANNEX I
                                                                    Page 1

                         ANNEX FOR TRANCHE C SUPPLEMENT

                                     ANNEX I

1.       Name and Date of Credit Agreement:

         Credit  Agreement,  dated as of  September  26,  1997 and  amended  and
         restated as of March 10, 1998,  among Extended Stay America,  Inc., the
         lenders from time to time party thereto, Morgan Stanley Senior Funding,
         Inc., as Syndication Agent and as Arranger,  and The Industrial Bank of
         Japan,  Limited,  as  Administrative  Agent,  including any amendments,
         modifications,  extensions,  renewals,  replacements,  restatements  or
         supplements thereto.

2.       Supplement Effective Date:

         December 15, 1998 (the "Supplement Effective Date")

3. Amounts (as of date of item #2 above):

                                       Commitment Under Relevant
        Bank                          Tranche C Term Loan Sub-Facility

        Archimedes Funding II, Ltd.                $  8,000,000
        KZH ING-3 LLC                              $  2,000,000
        KZH ING-1 LLC                              $  5,000,000
        The Industrial Bank of Japan, Ltd.         $ 11,000,000
        KZH Sterling, LLC                          $  5,000,000
        Franklin Floating Rate Trust               $ 10,000,000
        Pilgrim Prime Rate Trust                   $  5,000,000
        Morgan Stanley Senior Funding, Inc.        $ 54,000,000

        Total Commitment                           $100,000,000
                                                   ============

4. Maturity Date for Relevant Tranche C Term Loan Sub-Facility:

   December 31, 2004 (the "C Maturity Date")

5. Scheduled Amortizations:

                  In addition to any other  mandatory  repayments  or commitment
         reductions  pursuant  to  Section  4.02 of the  Credit  Agreement,  the
         Borrower  shall be  required  to repay on each date set forth below the
         principal   amount  of  the  Tranche  C  Term  Loans,   to  the  extent
         outstanding,  set forth  opposite such date (each such repayment as the
         same may be reduced as provided in Section  4.01 and 4.02(h) and (i), a
         "Tranche C Term Loan Scheduled Repayment"):
<PAGE>

                                                                         ANNEX I
                                                                          Page 2

Tranche C Scheduled Repayment Date              Amount

Each December 31 commencing December 31, 2000   An amount equal to 1% of the    
and ended December 31, 2003                     aggregate principal amount of
                                                Tranche C Term Loans outstanding
                                                on the last date of the Tranche 
                                                C Drawing Period (as defined 
                                                below)
 


Each March 21, 2004, June 30, 2004, September   An amount equal to 24% of the   
30, 2004 and the C Maturity Date                aggregate principal amount of  
                                                Tranche C Term Loans outstanding
                                                on the last day of the Tranche C
                                                Drawing Period                
      
      
      
      
      


6.   Applicable C Margin:

          For Base Rate Loans:  2.50%;
          For Eurodollar Loans: 3.50%.

7.   Commitment  Commission:  The Borrower agrees to pay to the  Administrative
     Agent for distribution to each Tranche C Bank with a Tranche C Term Loan  
     Commitment a commitment  commission  (the  "Tranche C Term Loan Commitment
     Commission")  for the period from the Supplement  Effective Date to but not
     including the last day of the  Tranche C  Drawing  Period  computed  at a 
     rate per annum for each day equal to3/4of 1% on the Tranche  C Term  Loan 
     Commitment  of such  Tranche  C Bank on  such  day.  Accrued  Tranche  C 
     Term  Loan Commitment  Commission  shall be due and payable  quarterly in
     arrears on each Quarterly  Payment Date and on the last day of the Tranche
     C Drawing  Period or such earlier date upon which the Total  Tranche C Term
     Loan Commitment is terminated.

8.   Facility  Fee;  Other Fees:  The Borrower  shall pay to the Agents such
     other fees as have been separately agreed to in writing by the Borrower
     with the Agents with respect to the Tranche C Term Loan Commitment.

9.   Additional  Conditions  Precedent  to the  Supplement  Effective  Date.
     Except as otherwise set forth below,  the  occurrence of the Supplement
     Effective Date is subject at the time of occurrence to the satisfaction
     of the following conditions:

                  9.01  Execution of  Agreement;  Notes.  (i) On or prior to the
         Supplement  Effective Date (i) this Agreement  shall have been executed
         and  delivered as provided in paragraph 4, (ii) an  Acknowledgment  and
         Agreement in the form of Annex II to this Supplement  shall be executed
         and delivered to the Administrative  Agent by each
<PAGE>

                                                                         ANNEX I
                                                                          Page 3

         Subsidiary Guarantor and (iii) there shall have been delivered to the
         Administrative  Agent for the account of each of the Tranche C Banks 
         the appropriate  Tranche C Term Note  executed  by the  Borrower,  in
         each  case in the  amount, maturity and as otherwise provided herein.

                  9.02 Fees, etc. On or prior to the Supplement  Effective Date,
         the Borrower shall have paid to the Agents and the Banks all reasonable
         costs, fees and expenses  (including,  without  limitation,  reasonable
         legal fees and expenses) payable to the respective Agents and the Banks
         to the extent then due.

                  9.03 Opinion of Counsel. (a) On the Supplement Effective Date,
         the  Administrative  Agent shall have received from Bell, Boyd & Lloyd,
         counsel  to the  Borrower  and the  Subsidiary  Guarantors,  an opinion
         addressed  to each of the  Agents  and each of the  Banks and dated the
         Supplement  Effective  Date covering the matters set forth in Annex III
         to this Supplement and such other matters  incident to the transactions
         contemplated herein as either Agent may reasonably request.

                  (b) To the extent that any condition  precedent required to be
         satisfied  under  9.03 (a)  above is not  satisfied  on the  Supplement
         Effective  Date, the  satisfaction  of such shall be solely a condition
         precedent to the  incurrence of the Tranche C Term Loans on the initial
         Borrowing date.

                  9.04  Corporate  Documents;   Proceedings;  etc.  (a)  On  the
         Supplement Effective Date, the Administrative Agent shall have received
         a  certificate,  dated the  Supplement  Effective  Date,  signed by the
         chairman  of the  board,  the  president,  any  vice  president  or the
         treasurer of the Borrower and each Subsidiary of the Borrower,  if any,
         which is to become a Credit Party on the Supplement Effective Date, and
         attested  to by  the  secretary  or  any  assistant  secretary  of  the
         respective  such  Person,  in the  form  of  Exhibit  F to  the  Credit
         Agreement  with  appropriate  insertions,  together  with copies of the
         certificate of incorporation and by-laws of the respective such Person,
         and the  resolutions of the respective  such Person referred to in such
         certificate,  and the foregoing  shall be reasonably  acceptable to the
         Agents.

                  (b) On the Supplement Effective Date, the Administrative Agent
         shall have received  certificates of all Credit Parties (other than the
         Credit Parties  delivering  certificates  pursuant to preceding  clause
         (a)) (x) certifying  that there were no changes,  or providing the text
         of any changes, to the certificate of incorporation and by-laws of such
         Credit  Parties as  delivered  pursuant  to Section  5.04 of the Credit
         Agreement,  (y) to the effect  that each such  Credit  Party is in good
         standing in its respective state of  incorporation  and in those states
         where each such Credit Party  conducts  business and (z)  providing the
         resolutions  adopted  by each such  Credit  Party  with  respect to the
         actions contemplated in this Agreement (including,  without limitation,
         with respect to the amendment and  restatement of this  Agreement,  and
         the  obligations  of such Credit  Party with  respect to the  increased
         extensions  of credit  pursuant  hereto),  and the  foregoing  shall be
         reasonably acceptable to the Agents in their reasonable discretion.
<PAGE>

                                                                         ANNEX I
                                                                          Page 4

                  (c)  On  or  prior  to  the  Supplement  Effective  Date,  all
         corporate,  and legal proceedings and all instruments and agreements in
         connection with the transactions contemplated by this Agreement and the
         other Credit  Documents  shall be reasonably  satisfactory  in form and
         substance  to the  Agents  and the  Banks,  and the  Agents  shall have
         received  all  information  and  copies of all  documents  and  papers,
         including   records   of   corporate   and   partnership   proceedings,
         governmental  approvals,  good  standing  certificates  and  bring-down
         telegrams,  if any,  which any Agent may have  reasonably  requested in
         connection therewith, such documents and papers where appropriate to be
         certified by proper corporate, or governmental authorities.

                  (d) To the extent that any condition  precedent required to be
         satisfied  under 9.04 (a),  (b), or (c) above is not  satisfied  on the
         Supplement  Effective Date, the  satisfaction of such shall be solely a
         condition  precedent to the  incurrence  of the Tranche C Term Loans on
         the initial Borrowing date.

                  9.05  Adverse  Change,  etc. (a) On the  Supplement  Effective
         Date,  nothing  shall have  occurred  (and the Banks  shall have become
         aware of no  facts,  conditions  or other  information  not  previously
         known)  which  any  Agent or the  Banks  believe  would  reasonably  be
         expected  to  have a  material  adverse  effect  (i) on the  rights  or
         remedies  of the Agents or the Banks,  or on the  ability of any Credit
         Party to perform its respective obligations to the Agents and the Banks
         or (ii) on the business,  operations,  property,  assets,  liabilities,
         condition (financial or otherwise) or prospects of the Borrower and its
         Subsidiaries taken as a whole.

                  (b)  On  or  prior  to  the  Supplement  Effective  Date,  all
         necessary governmental (domestic and foreign) and third party approvals
         and/or consents (if any) in connection with the making of the Tranche C
         Term Loans and the  transactions  contemplated by the Credit  Documents
         and  otherwise  referred to herein or therein  shall have been obtained
         and remain in effect,  and all  applicable  waiting  periods shall have
         expired without any action being taken by any competent authority which
         restrains,  prevents or imposes  materially adverse conditions upon the
         making of the Tranche C Term Loans and the transactions contemplated by
         the  Credit  Documents  or  otherwise  referred  to herein or  therein.
         Additionally,  there shall not exist any judgment, order, injunction or
         other restraint issued or filed or a hearing seeking  injunctive relief
         or  other  restraint  pending  or  notified   prohibiting  or  imposing
         materially  adverse  conditions  upon the making of the  Tranche C Term
         Loans or the transactions contemplated by the Credit Documents.

                  (c) On or  prior  to the  Supplement  Effective  Date,  (i) no
         Default or Event of Default  exists  and (ii) all  representations  and
         warranties contained in the Credit Agreement and other Credit Documents
         shall be true and correct in all material respects with the same effect
         as though  such  representations  and  warranties  had been made on the
         Supplement Effective Date.

                  9.06  Litigation.   On  the  Supplement   Effective  Date,  no
         litigation by any entity (private or governmental) shall be pending or,
         to the best of the Borrower's knowledge,
<PAGE>

                                                                         ANNEX I
                                                                          Page 5

         threatened with respect to the making of the  Tranche  C Term  Loans or
         any  Loans  under  the  Credit Agreement  or the Credit  Documents  or
         any  documentation  executed in connection therewith or the 
         transactions contemplated thereby.

                  9.07   Conditions   under  Section  1.14.  On  the  Supplement
         Effective  Date, all conditions to the  establishment  of the Tranche C
         Term Loan Facility specified under Section 1.14 of the Credit Agreement
         shall have been satisfied.

10.      Additional  Conditions  Precedent to the  Incurrence  of Tranche C Term
         Loans:  In  addition  to the  conditions  set forth in Section 6 of the
         Credit Agreement, the obligation of each Tranche C Bank to make Tranche
         C Term Loans is  subject  at the time of the  making of such  Tranche C
         Term Loans to the satisfaction of the following conditions:

                  (a)  Tranche C Term  Loans may be  borrowed  from time to time
         after the later of (x) January 1, 1999 and (y) the Supplement Effective
         Date until  April 15, 1999 (such  period  being  herein  referred to as
         "Tranche C Drawing Period"), provided that the Tranche C Term Loans may
         not be borrowed on more than two dates; and

                  (b) The initial  aggregate  principal  amount of the Tranche C
         Term Loans shall not exceed the Maximum Tranche C Permitted Amount.

11.      Notice and Information:

                  MORGAN STANLEY SENIOR FUNDING, INC.

                  1585 Broadway
                  New York, NY 10036
                  Attention:     Mike McLaughlin
                  Telephone:     212-761-2838
                  Telecopier:    212-761-0322


                  ARCHIMEDES FUNDING II, LTD.

                  333 South Grand Avenue
                  Suite 4250
                  Los Angeles, CA 90071
                  Attention:   Mike Campbell
                  Telephone:  213-346-3971
                  Telecopier:  213-346-3995
<PAGE>

                                                                         ANNEX I
                                                                          Page 6

                  KZH ING-1 LLC

                  c/o The Chase Manhattan Bank
                  450 West 33rd Street - 15th Floor
                  New York, NY  10001
                  Attention:  Virginia Conway
                  Telephone:  212-946-7575
                  Telecopier:  212-946-7776


                  KZH ING-3 LLC

                  c/o The Chase Manhattan Bank
                  450 West 33rd Street - 15th Floor
                  New York, NY  10001
                  Attention:  Virginia Conway
                  Telephone:  212-946-7575
                  Telecopier:  212-946-7776


                  THE INDUSTRIAL BANK OF JAPAN, LTD.

                  1251 Avenue of the Americas
                  New York, NY 10020-1104
                  Attention:   Chris Droussiotis
                  Telephone:  212-282-3323
                  Telecopier:  212-282-4490


                  KZH STERLING LLC

                  c/o The Chase Manhattan Bank
                  450 West 33rd Street - 15th Floor
                  New York, NY  10001
                  Attention:  Virginia Conway
                  Telephone:  212-946-7575
                  Telecopier:  212-946-7776


                  FRANKLIN FLOATING RATE TRUST

                  777 Mariners Island Blvd.
                  San Mateo, CA 94404
                  Attention:   Chauncey Lufkin
                  Telephone:  650-525-7424
                  Telecopier:  650-312-3346
<PAGE>

                                                                         ANNEX I
                                                                          Page 7

                  PILGRIM PRIME RATE TRUST

                  Two Renaisance Square
                  40 N. Central Ave., Suite 1200
                  Phoenix, AZ 85004-4424
                  Attention:   Jeff Bakalar
                  Telephone:  602-417-8259
                  Telecopier:  602-417-8327