<PAGE>

                                                                   Exhibit 4.13

                         FIRST SUPPLEMENTAL INDENTURE

          This "Supplemental Indenture," dated as of January 26, 2001, among
each of the subsidiaries of MeriStar Hospitality Corporation, a Maryland
corporation (the "Company"), indicated as signatories hereto (collectively, the
"Guarantors" and each, a "Guarantor") and The Bank of New York (as successor to
IBJ Whitehall Bank & Trust Company), as trustee under the indenture referred to
below (the "Trustee").

                              W I T N E S S E T H

          WHEREAS, the Company has heretofore executed and delivered to the
Trustee an indenture (the "Indenture"), dated as of March 18, 1999 providing for
the issuance of up to an aggregate principal amount of $55,000,000 of 8 3/4%
Senior Subordinated Notes due 2007 (the "Notes");

          WHEREAS, Section 4.15 of the Indenture provides that under certain
circumstances the Company is required to cause the Guarantors to execute and
deliver to the Trustee a supplemental indenture pursuant to which the Guarantors
shall unconditionally guarantee all of the Company's Obligations under the Notes
pursuant to a Guarantee on the terms and conditions set forth herein; and

          WHEREAS, pursuant to Section 9.1 of the Indenture, the Trustee is
authorized to execute and deliver this Supplemental Indenture.

          NOW THEREFORE, in consideration of the foregoing and for other good
and valuable consideration, the receipt of which is hereby acknowledged, the
Guarantors and the Trustee mutually covenant and agree for the equal and ratable
benefit of the Holders of the Notes as follows:

          1.   CAPITALIZED TERMS.  Capitalized terms used herein without
definition shall have the meanings assigned to them in the Indenture.

          2.   AGREEMENT TO GUARANTEE.  The Guarantors hereby agree, jointly and
severally with all other Guarantors, to guarantee the Company's obligations
under the Notes on the terms and subject to the conditions set forth in Article
11 of the Indenture and to be bound by all other applicable provisions of the
Indenture. The obligations of the Guarantors hereunder shall be junior and
subordinated to the Senior Debt of such Guarantors in the manner and to the
extent set forth in Article 11 of the Indenture.

          3.   NO RECOURSE AGAINST OTHERS.  No past, present or future director,
officer, employee, incorporator, shareholder or agent of the Guarantors, as
such, shall have any liability for any obligations of the Company or any
Guarantors under the Notes, any Guarantees, the Indenture or this Supplemental
Indenture or for any claim based on, in respect of, or by reason of, such
obligations or their creation. Each Holder
<PAGE>

of the Notes by accepting a Note waives and releases all such liability. The
waiver and release are part of the consideration for issuance of the Notes. Such
waiver or release may not be effective to waive or release liabilities under the
federal securities laws.

          4.   NEW YORK LAW TO GOVERN.  The internal law of the State of New
York shall govern and be used to construe this Supplemental Indenture.

          5.   COUNTERPARTS.  The parties may sign any number of copies of this
Supplemental Indenture. Each signed copy shall be an original, but all of them
together represent the same agreement.

          6.   EFFECT OF HEADINGS.  The Section headings herein are for
convenience only and shall not affect thse construction hereof.
<PAGE>

          IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed and attested, all as of the date first above
written.

Dated: January 26, 2001


                              GUARANTORS:

                              MERISTAR HOSPITALITY OPERATING
                              PARTNERSHIP, L.P.,
                              a Delaware limited partnership

                              By:  MeriStar Hospitality Corporation, a
                                   Maryland corporation, general partner

                                   By:  /s/ Christopher L. Bennett
                                        -------------------------------
                                        Christopher L. Bennett
                                        Vice President, Legal

                              MERISTAR HOSPITALITY FINANCE CORP.
                              a Delaware corporation

                              By:  /s/ Christopher L. Bennett
                                   --------------------------------
                                   Christopher L. Bennett
                                   Vice President, Legal

                              MERISTAR ACQUISITION COMPANY, L.L.C.,
                              a Delaware limited liability company

                              By:  MeriStar Hospitality Operating Partnership,
                                   L.P.,
                                   a Delaware limited partnership, member

                                   By:  MeriStar Hospitality Corporation, a
                                        Maryland corporation, general partner

                                        By:  /s/ Christopher L. Bennett
                                             --------------------------------
                                             Christopher L. Bennett
                                             Vice President, Legal
<PAGE>

                              AGH PSS I, INC.,
                              a Delaware corporation

                              By:  /s/ Christopher L. Bennett
                                   -------------------------------
                                   Christopher L. Bennett
                                   Vice President, Legal

                              AGH UPREIT LLC,
                              a Delaware limited liability company

                              By:  MeriStar Hospitality Corporation, a
                                   Maryland corporation, member

                                   By:  /s/ Christopher L. Bennett
                                        -------------------------------
                                        Christopher L. Bennett
                                        Vice President, Legal

                              By:  MeriStar Hospitality Operating Partnership,
                                   L.P.,
                                   a Delaware limited partnership, member

                                   By:  MeriStar Hospitality Corporation, a
                                        Maryland corporation, general partner

                                        By:  /s/ Christopher L. Bennett
                                             -------------------------------
                                             Christopher L. Bennett
                                             Vice President, Legal
<PAGE>

                    CAPSTAR HOUSTON SW PARTNERS, L.P.
                    CAPSTAR MEDALLION HOUSTON PARTNERS, L.P.
                    CAPSTAR MEDALLION DALLAS PARTNERS, L.P.
                    CAPSTAR MEDALLION AUSTIN PARTNERS, L.P.
                    CAPSTAR MIDLAND PARTNERS, L.P.
                    CAPSTAR DALLAS PARTNERS, L.P.
                    CAPSTAR MOCKINGBIRD PARTNERS, L.P.
                    Each of the above being a Delaware limited partnership

                    By:  MeriStar Hospitality Operating Partnership, L.P.,
                         a Delaware limited partnership, general partner

                         By:  MeriStar Hospitality Corporation, a
                              Maryland corporation, general partner

                              By:  /s/ Christopher L. Bennett
                                   -------------------------------
                                   Christopher L. Bennett
                                   Vice President, Legal
<PAGE>

                    EQUISTAR SCHAUMBURG COMPANY, L.L.C.
                    EQUISTAR BELLEVUE COMPANY, L.L.C.
                    EQUISTAR CLEVELAND COMPANY, L.L.C.
                    EQUISTAR LATHAM COMPANY, L.L.C.
                    EQUISTAR VIRGINIA COMPANY, L.L.C.
                    EQUISTAR BALLSTON COMPANY, L.L.C.
                    EQUISTAR SALT LAKE COMPANY, L.L.C.
                    EQUISTAR ATLANTA GP COMPANY, L.L.C.
                    EQUISTAR ATLANTA LP COMPANY, L.L.C.
                    CAPSTAR WASHINGTON COMPANY, L.L.C.
                    CAPSTAR CS COMPANY, L.L.C.
                    CAPSTAR SAN PEDRO COMPANY, L.L.C.
                    CAPSTAR LOUISVILLE COMPANY, L.L.C.
                    CAPSTAR LEXINGTON COMPANY, L.L.C.
                    CAPSTAR OKLAHOMA CITY COMPANY, L.L.C.
                    CAPSTAR CHERRY HILL COMPANY, L.L.C.
                    CAPSTAR FRAZER COMPANY, L.L.C.
                    CAPSTAR KC COMPANY, L.L.C.
                    CAPSTAR NATIONAL AIRPORT COMPANY, L.L.C.
                    CAPSTAR GEORGETOWN COMPANY, L.L.C.
                    CAPSTAR JEKYLL COMPANY, L.L.C.
                    CAPSTAR DETROIT AIRPORT COMPANY, L.L.C.
                    CAPSTAR TUCSON COMPANY, L.L.C.
                    CAPSTAR MESA COMPANY, L.L.C.
                    CAPSTAR MORRISTOWN COMPANY, L.L.C.
                    CAPSTAR INDIANAPOLIS COMPANY, L.L.C.
                    CAPSTAR CHICAGO COMPANY, L.L.C.
                    CAPSTAR WINDSOR LOCKS COMPANY, L.L.C.
                    CAPSTAR HARTFORD COMPANY, L.L.C.
                    CAPSTAR CROSS KEYS COMPANY, L.L.C.
                    CAPSTAR COLUMBIA COMPANY, L.L.C.
                    CAPSTAR ROLAND PARK COMPANY, L.L.C.
                    CAPSTAR FORRESTAL COMPANY, L.L.C.
                    Each of the above being a Delaware limited liability company

                    By:  MeriStar Hospitality Operating Partnership, L.P.,
                         a Delaware limited partnership, member

                         By:  MeriStar Hospitality Corporation, a
                              Maryland corporation, general partner

                              By:  /s/ Christopher L. Bennett
                                   -------------------------------
                                   Christopher L. Bennett
                                   Vice President, Legal
<PAGE>

                    MERISTAR SANTA BARBARA COMPANY, L.P.
                    MERISTAR LAJV COMPANY, L.P.
                    MERISTAR CATHEDRAL CITY COMPANY, L.P.
                    Each of the above being a Delaware limited partnership

                    By:  MeriStar Hospitality Operating Partnership, L.P.,
                         a Delaware limited partnership, general partner

                         By:  MeriStar Hospitality Corporation, a
                              Maryland corporation, general partner

                              By:  /s/ Christopher L. Bennett
                                   -------------------------------
                                   Christopher L. Bennett
                                   Vice President, Legal

                    MERISTAR SANIBEL INN COMPANY, LLC
                    MERISTAR SUNDIAL BEACH COMPANY, LLC
                    MERISTAR SAFETY HARBOR COMPANY, LLC
                    MERISTAR SEASIDE INN COMPANY, LLC
                    MERISTAR PLANTATION SHOPPING CENTER COMPANY, LLC
                    MERISTAR SONG OF THE SEA COMPANY, LLC
                    MERISTAR SHIRLEY'S PARCEL COMPANY, LLC
                    MERISTAR SANIBEL GOLF COMPANY, LLC
                    MERISTAR MARCO ISLAND COMPANY, LLC
                    MERISTAR S.S. PLANTATION COMPANY, LLC
                    MERISTAR HOTEL (CALGARY AIRPORT) LLC
                    MERISTAR HOTEL (VANCOUVER) LLC
                    MERISTAR HOTEL (SURREY) LLC
                    MERISTAR HOTEL (BURNABY) LLC
                    AGH 75 ARLINGTON HEIGHTS LLC
                    Each of the above being a Delaware limited liability company

                    By:  MeriStar Hospitality Operating Partnership, L.P.,
                         a Delaware limited partnership, member

                         By:  MeriStar Hospitality Corporation, a
                              Maryland corporation, general partner

                              By:  /s/ Christopher L. Bennett
                                   -------------------------------
                                   Christopher L. Bennett
                                   Vice President, Legal
<PAGE>

                    75 ARLINGTON HEIGHTS LIMITED PARTNERSHIP, L.P.,
                    a Delaware limited partnership

                    By:  AGH 75 Arlington Heights LLC,
                         A Delaware limited liability company, general partner

                         By:  MeriStar Hospitality Operating Partnership, L.P.,
                              a Delaware limited partnership, member

                              By:  MeriStar Hospitality Corporation, a
                                   Maryland corporation, general partner

                                   By:  /s/ Christopher L. Bennett
                                        -------------------------------
                                        Christopher L. Bennett
                                        Vice President, Legal

                         BCHI ACQUISITION, LLC
                         a Delaware limited liability company

                         By:  AGH UPREIT LLC,
                              a Delaware limited liability company, member

                              By:  MeriStar Hospitality Operating Partnership,
                                   L.P., a Delaware limited partnership, member

                                   By:  MeriStar Hospitality Corporation,
                                        a Maryland corporation, general partner

                                        By:  /s/ Christopher L. Bennett
                                             -------------------------------
                                             Christopher L. Bennett
                                             Vice President, Legal

                         By:  MeriStar Hospitality Operating Partnership, L.P.,
                              a Delaware limited partnership, member

                              By:  MeriStar Hospitality Corporation,
                                   a Maryland corporation, general partner

                              By:  /s/ Christopher L. Bennett
                                   -------------------------------
                                   Christopher L. Bennett
                                   Vice President, Legal
<PAGE>

                    MDV LIMITED PARTNERSHIP
                    a Texas limited partnership

                    183 HOTEL ASSOCIATES, LTD.
                    a Texas limited partnership

                    LAKE BUENA VISTA PARTNERS, LTD.
                    a Florida limited partnership

                    DURHAM I-85 LIMITED PARTNERSHIP
                    a Delaware limited partnership

                    COCOA BEACH HOTELS, LTD.
                    a Florida limited partnership

                    By:  AGH UPREIT LLC, a Delaware limited liability
                         company, their general partner

                         By:  MeriStar Hospitality Operating Partnership,
                              L.P., a Delaware limited partnership, member

                              By:  MeriStar Hospitality Corporation, a
                                   Maryland corporation, general partner

                                   By:  /s/ Christopher L. Bennett
                                        -------------------------------
                                        Christopher L. Bennett
                                        Vice President, Legal

                    MERISTAR HOTEL LESSEE, INC.,
                    a Delaware corporation


                    By:  /s/ Christopher L. Bennett
                         -------------------------------
                         Christopher L. Bennett
                         Vice President, Legal
<PAGE>

                    HOTEL COLUMBIA COMPANY,
                    a Maryland general partnership


                    By:  CapStar Columbia Company, L.L.C.,
                         a Delaware limited liability company, partner

                         By:  MeriStar Hospitality Operating Partnership, L.P.,
                              a Delaware limited partnership, member

                              By:  MeriStar Hospitality Corporation, a
                                   Maryland corporation, general partner

                                   By:  /s/ Christopher L. Bennett
                                        -------------------------------
                                        Christopher L. Bennett
                                        Vice President, Legal

                    By:  CapStar Roland Park Company, L.L.C., a
                         Delaware limited liability company, partner

                         By:  MeriStar Hospitality Operating Partnership, L.P.,
                              a Delaware limited partnership, member

                              By:  MeriStar Hospitality Corporation, a
                                   Maryland corporation, general partner

                                   By:  /s/ Christopher L. Bennett
                                        -------------------------------
                                        Christopher L. Bennett
                                        Vice President, Legal

                    MERISTAR LP, INC.,
                    a Nevada corporation


                    By:  /s/ Christopher L. Bennett
                         -------------------------------
                         Christopher L. Bennett
                         Vice President, Legal
<PAGE>

                    3100 GLENDALE JOINT VENTURE
                    an Ohio general partnership

                    By:  AGH UPREIT LLC,
                         a Delaware limited liability company, partner

                         By:  MeriStar Hospitality Operating Partnership, L.P.,
                              a Delaware limited partnership, member

                              By:  MeriStar Hospitality Corporation, a
                                   Maryland corporation, general partner

                                   By:  /s/ Christopher L. Bennett
                                        -------------------------------
                                        Christopher L. Bennett
                                        Vice President, Legal

                    By:  MeriStar Hospitality Operating Partnership, L.P.,
                         a Delaware limited partnership, partner

                         By:  MeriStar Hospitality Corporation, a
                              Maryland corporation, general partner

                              By:  /s/ Christopher L. Bennett
                                   -------------------------------
                                   Christopher L. Bennett
                                   Vice President, Legal

                    THE BANK OF NEW YORK,
                    as Trustee

                    By:  /s/ Ming J. Shiang
                         -------------------------------
                         Name:  Ming J. Shiang
                         Title: Vice President