Document:

<PAGE>   1
                                                                   EXHIBIT 4.7.8

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

                               AMFM OPERATING INC.

                                   AS OBLIGOR

                                       AND

                           THE GUARANTORS NAMED HEREIN

                                       AND

                       U.S. TRUST COMPANY OF TEXAS, N.A.,

                                   AS TRUSTEE

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

                         SEVENTH SUPPLEMENTAL INDENTURE

                          DATED AS OF JANUARY 18, 2000

                                       TO

                                    INDENTURE

                          DATED AS OF FEBRUARY 14, 1996

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

                                  $200,000,000

                    9 3/8% SENIOR SUBORDINATED NOTES DUE 2004

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

<PAGE>   2

         SEVENTH SUPPLEMENTAL INDENTURE dated as of January 18, 2000, among AMFM
OPERATING INC., a Delaware corporation (the "Company"), the subsidiaries listed
on Schedule I hereto (collectively, the "New Subsidiary Guarantors") and U.S.
TRUST COMPANY OF TEXAS, N.A., a national banking association, as Trustee (the
"Trustee").

         WHEREAS, Chancellor Radio Broadcasting Company ("CRBC") (which, prior
to February 14, 1996, was known as Chancellor Broadcasting Company) and
Chancellor Broadcasting Licensee Company have heretofore executed and delivered
to the Trustee an Indenture dated as of February 14, 1996, as amended by that
certain First Supplemental Indenture dated as of February 14, 1996 by and among
CRBC, the guarantors named therein and the Trustee, by that certain Second
Supplemental Indenture dated as of April 15, 1997 by and among CRBC, the
guarantors named therein and the Trustee, by that certain Third Supplemental
Indenture dated as of September 5, 1997 by and among Chancellor Media
Corporation of Los Angeles ("CMCLA"), the guarantors named therein and the
Trustee, by that certain Fourth Supplemental Indenture dated as of October 28,
1997 by and among CMCLA, the guarantors named therein and the Trustee, by that
certain Fifth Supplemental Indenture dated as of August 23, 1999 by and among
CMCLA, the guarantors named therein and the Trustee, and by that certain Sixth
Supplemental Indenture dated as of November 19, 1999 by and among the Company,
the guarantors named therein and the Trustee (as so amended, the "Indenture"),
providing for the issuance of $200,000,000 aggregate principal amount of 9 3/8%
Senior Subordinated Notes due 2004 (the "Notes");

         WHEREAS, pursuant to that Third Supplemental Indenture, dated as of
September 5, 1997, CMCLA assumed the obligations under the Notes and the
Indenture, and CMCLA and the Trustee amended certain other terms of the
Indenture;

         WHEREAS, pursuant to that Sixth Supplemental Indenture, dated as of
November 19, 1999, the Company assumed the obligations under the Notes and the
Indenture;

         WHEREAS, the Company, the New Subsidiary Guarantors and the Trustee
desire by this Seventh Supplemental Indenture pursuant to and as contemplated by
the provisions of the Indenture relating to the addition of guarantors,
including Sections 4.19 and 10A.03, to add the New Subsidiary Guarantors as
guarantors.

         WHEREAS, the execution and delivery of this Seventh Supplemental
Indenture has been authorized by resolutions of the Boards of Directors of the
Company and each of the New Subsidiary Guarantors (and in the case of any
guarantor that is a limited partnership or a limited liability company, the
Board of Directors of the general partner or sole member, respectively); and

         WHEREAS, all conditions and requirements necessary to make this Seventh
Supplemental Indenture a valid, binding legal instrument in accordance with its
terms have been performed and fulfilled by the parties hereto and the execution
and delivery thereof have been in all respects duly authorized by the parties
hereto.

         NOW, THEREFORE, in consideration of the above premises, each party
agrees, for the benefit of the others and for the equal and ratable benefit of
the holders of the Notes, as follows:

<PAGE>   3

                                    ARTICLE I

                     ASSUMPTION OF OBLIGATIONS AS GUARANTOR

         Section 1.01 ASSUMPTION. Each of the New Subsidiary Guarantors hereby
expressly and unconditionally assumes each and every covenant, agreement and
undertaking of a Guarantor in the Indenture as of the date of this Seventh
Supplemental Indenture, and also hereby expressly and unconditionally assumes
each and every covenant, agreement and undertaking of a Guarantor in each Note
outstanding on the date of this Seventh Supplemental Indenture.

                                   ARTICLE II

                            MISCELLANEOUS PROVISIONS

         Section 2.01 DEFINED TERMS. For all purposes of this Seventh
Supplemental Indenture, except as otherwise defined or unless the context
otherwise requires, terms used in capitalized form in this Seventh Supplemental
Indenture and defined in the Indenture have the meanings specified in the
Indenture.

         Section 2.02 INDENTURE. Except as amended hereby, the Indenture and the
Notes are in all respects ratified and confirmed and all the terms shall remain
in full force and effect.

         Section 2.03 GOVERNING LAW. THIS SEVENTH SUPPLEMENTAL INDENTURE SHALL
BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW
YORK, AS APPLIED TO CONTRACTS MADE AND PERFORMED WITHIN THE STATE OF NEW YORK,
WITHOUT REGARD TO PRINCIPLES OF CONFLICT OF LAWS.

         Section 2.04 SUCCESSORS. All agreements of the Company and the New
Subsidiary Guarantors in this Seventh Supplemental Indenture and the Notes shall
bind their successors. All agreements of the Trustee in this Seventh
Supplemental Indenture shall bind its successors.

         Section 2.05 DUPLICATE ORIGINALS. All parties may sign any number of
copies of this Seventh Supplemental Indenture. Each signed copy shall be an
original, but all of them together shall represent the same agreement.

         Section 2.06 SEVERABILITY. In case any one or more of the provisions in
this Seventh Supplemental Indenture or in the Notes shall be held invalid,
illegal or unenforceable, in any respect for any reason, the validity, legality
and enforceability of any such provision in every other respect and of the
remaining provisions shall not in any way be affected or impaired thereby, it
being intended that all of the provisions hereof shall be enforceable to the
full extent permitted by law.

                                        2

<PAGE>   4

         Section 2.07 TRUSTEE DISCLAIMER. The Trustee accepts the amendment of
the Indenture effected by this Seventh Supplemental Indenture and agrees to
execute the trust created by the Indenture as hereby amended, but on the terms
and conditions set forth in the Indenture, including the terms and provisions
defining and limiting the liabilities and responsibilities of the Trustee, which
terms and provisions shall in like manner define and limit its liabilities and
responsibilities in the performance of the trust created by the Indenture as
hereby amended, and without limiting the generality of the foregoing, the
Trustee shall not be responsible in any manner whatsoever for or with respect to
any of the recitals or statements contained herein, all of which recitals or
statements are made solely by the Company and the New Subsidiary Guarantors, or
for or with respect to (i) the validity or sufficiency of this Seventh
Supplemental Indenture or any of the terms or provisions hereof, (ii) the proper
authorization hereof by the Company and the New Subsidiary Guarantors by
corporate action or otherwise, (iii) the due execution hereof by the Company and
the New Subsidiary Guarantors or (iv) the consequences (direct or indirect and
whether deliberate or inadvertent) of any amendment herein provided for, and the
Trustee makes no representation with respect to any such matters.

         Section 2.08 EFFECTIVENESS. This Seventh Supplemental Indenture shall
become effective, once executed, upon receipt by the Trustee of a certificate of
the appropriate officers of the Company and an opinion of Vinson & Elkins
L.L.P., counsel to the Company, each of which shall be dated no earlier than the
date hereof.

            [THE REMAINDER OF THIS PAGE IS INTENTIONALLY LEFT BLANK]

                                        3

<PAGE>   5

         IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed as of the day and year written above.

                                      AMFM OPERATING INC.,
                                      as Obligor

                                      By: /s/ W. Schuyler Hansen
                                         --------------------------------------
                                         W. Schuyler Hansen
                                         Senior Vice President and Chief
                                           Accounting Officer

Attest:  /s/
       --------------------------

                                      ON BEHALF OF EACH OF THE NEW SUBSIDIARY
                                      GUARANTORS LISTED ON SCHEDULE I HERETO*

                                      By:  /s/ Kathy Archer
                                         --------------------------------------
                                         Kathy Archer
                                         Senior Vice President

Attest:  /s/
       --------------------------

                                      U.S. TRUST COMPANY OF TEXAS, N.A.,
                                      as Trustee

                                       /s/ Bill Barber
                                      -----------------------------------------
                                      By:  Bill Barber
                                         --------------------------------------
                                      Title:  Vice President
                                             ----------------------------------

Attest:  /s/
       --------------------------

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

*For AMFM LA, LLC, by the Company, its sole member. For AMFM Texas, LLC, by
Chancellor Media/Shamrock Broadcasting, Inc., its sole member.

<PAGE>   6

                                   SCHEDULE I

                            NEW SUBSIDIARY GUARANTORS

AMFM San Diego, Inc., a Delaware corporation
AMFM Washington D.C., Inc., a Delaware corporation
AMFM LA, LLC, a Delaware limited liability company
AMFM Texas, LLC, a Delaware limited liability company<PAGE>   1
                                                                   EXHIBIT 4.8.3

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

                   CHANCELLOR MEDIA CORPORATION OF LOS ANGELES

                                   as Obligor

                                       AND

                           the Guarantors named herein

                                       AND

                        U.S. TRUST COMPANY OF TEXAS, N.A.

                                   as Trustee

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

                          SECOND SUPPLEMENTAL INDENTURE

                          Dated as of October 28, 1997

                                       to

                                    Indenture

                            Dated as of June 24, 1997

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

                                  $200,000,000

                        8-3/4% Senior Subordinated Notes

                                    due 2007

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

<PAGE>   2

         SECOND SUPPLEMENTAL INDENTURE dated as of October 28, 1997, among
CHANCELLOR MEDIA CORPORATION OF LOS ANGELES, a Delaware corporation (the
"Company"), the subsidiaries signatories hereto (collectively, the "New
Subsidiary Guarantors") and U.S. TRUST COMPANY OF TEXAS, N.A., a national
banking association, as Trustee (the "Trustee").

         WHEREAS, Chancellor Radio Broadcasting Company ("CRBC") and the
guarantors named therein have executed and delivered to the Trustee an Indenture
dated as of June 24, 1997, as amended by that certain First Supplemental
Indenture dated as of September 5, 1997 (as amended, the "Indenture"), providing
for the issuance of $200,000,000 aggregate principal amount of 8-3/4% Senior
Subordinated Notes due 2007 (the "Notes"); and

         WHEREAS, pursuant to that certain Amended and Restated Agreement and
Plan of Merger by and among Chancellor Broadcasting Company, CRBC, Evergreen
Media Corporation, Evergreen Mezzanine Holdings Corporation and Evergreen Media
Corporation of Los Angeles, dated as of February 19, 1997 and amended and
restated as of July 31, 1997 (the Merger Agreement"), among other things, (i)
Chancellor Broadcasting Company merged with and into Evergreen Mezzanine
Holdings Corporation (the "Parent Merger") and (ii) CRBC merged with and into
Evergreen Media Corporation of Los Angeles (the "Subsidiary Merger"). Upon
completion of the Parent Merger, Evergreen Media Corporation changed its name to
Chancellor Media Corporation and Evergreen Mezzanine Holdings Corporation
changed its name to Chancellor Mezzanine Holdings Corporation. Upon completion
of the Subsidiary Merger, Evergreen Media Corporation of Los Angeles changed its
name to Chancellor Media Corporation of Los Angeles; and

         WHEREAS, pursuant to that First Supplemental Indenture dated as of
September 5, 1997, the Company assumed the obligations under the Notes and the
Indenture and the Company and the Trustee amended certain other terms of the
Indenture; and

         WHEREAS, the Company, the New Subsidiary Guarantors and the Trustee
desire by this Second Supplemental Indenture, pursuant to and as contemplated by
Sections 4.19 and 10A.03 of the Indenture, to add the New Subsidiary Guarantors
as guarantors pursuant to the terms of the Indenture; and

         WHEREAS, the execution and delivery of this Second Supplemental
Indenture has been authorized by resolutions of the Boards of Directors of the
Company and each of the New Subsidiary Guarantors; and

         WHEREAS, all conditions and requirements necessary to make this Second
Supplemental Indenture a valid, binding legal instrument in accordance with its
terms have been performed and fulfilled by the parties hereto and the execution
and delivery thereof have been in all respects duly authorized by the parties
hereto.

<PAGE>   3

         NOW, THEREFORE, in consideration of the above premises, each party
agrees, for the benefit of the others and for the equal and ratable benefit of
the holders of the Notes, as follows:

                                   ARTICLE I

                     ASSUMPTION OF OBLIGATIONS AS GUARANTOR

Section 1.01 Assumption. Each of the New Subsidiary Guarantors hereby expressly
and unconditionally assumes each and every covenant, agreement and undertaking
of a Guarantor in the Indenture as of the date of this Second Supplemental
Indenture, and also hereby expressly and unconditionally assumes each and every
covenant, agreement and undertaking of a Guarantor in each Note outstanding on
the date of this Second Supplemental Indenture.

                                  ARTICLE II

                            MISCELLANEOUS PROVISIONS

Section 2.01 Terms Defined. For all purposes of this Second Supplemental
Indenture, except as otherwise defined or unless the context otherwise requires,
terms used in capitalized form in this Second Supplemental Indenture and defined
in the Indenture have the meanings specified in the Indenture.

Section 2.02 Indenture. Except as amended hereby, the Indenture and the Notes
are in all respects ratified and confirmed and all the terms shall remain in
full force and effect.

Section 2.03 Governing Law. THIS SECOND SUPPLEMENTAL INDENTURE SHALL BE GOVERNED
BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, AS
APPLIED TO CONTRACTS MADE AND PERFORMED WITHIN THE STATE OF NEW YORK, WITHOUT
REGARD TO PRINCIPLES OF CONFLICT OF LAWS.

Section 2.04 Successors. All agreements of the Company and the New Subsidiary
Guarantors in this Second Supplemental Indenture and the Notes shall bind their
successors. All agreements of the Trustee in this Second Supplemental Indenture
shall bind its successors.

Section 2.05 Duplicate Originals. All parties may sign any number of copies of
this Second Supplemental Indenture. Each signed copy shall be an original, but
all of them together shall represent the same agreement.

Section 2.06 Severability. In case any one or more of the provisions in this
Second Supplemental Indenture or in the Notes shall be held invalid, illegal or
unenforceable, in any respect for any reason, the validity, legality and
enforceability of any such provision in every other respect and of the remaining
provisions shall not in any way be affected or impaired thereby, it being
intended that all of the provisions hereof shall be enforceable to the full
extent permitted by law.

<PAGE>   4

Section 2.07 Trustee Disclaimer. The Trustee accepts the amendment of the
Indenture effected by this Second Supplemental Indenture and agrees to execute
the trust created by the Indenture as hereby amended, but on the terms and
conditions set forth in the Indenture, including the terms and provisions
defining and limiting the liabilities and responsibilities of the Trustee, which
terms and provisions shall in like manner define and limit its liabilities and
responsibilities in the performance of the trust created by the Indenture as
hereby amended, and without limiting the generality of the foregoing, the
Trustee shall not be responsible in any manner whatsoever for or with respect to
any of the recitals or statements contained herein, all of which recitals or
statements are made solely by the Company and the New Subsidiary Guarantors, or
for or with respect to (i) the validity or sufficiency of this Second
Supplemental Indenture or any of the terms or provisions hereof, (ii) the proper
authorization hereof by the Company and the New Subsidiary Guarantors by
corporate action or otherwise, (iii) the due execution hereof by the Company and
the New Subsidiary Guarantors or (iv) the consequences (direct or indirect and
whether deliberate or inadvertent) of any amendment herein provided for, and the
Trustee makes no representation with respect to any such matters.

Section 2.08 Effectiveness.

         (a) This Second Supplemental Indenture shall become effective once
         executed upon fulfillment of the conditions set forth in Section
         2.08(b) below.

         (b) This Second Supplemental Indenture shall not become effective until
         receipt by the Trustee of the following, in each case dated no earlier
         than the date hereof.

                  (i) a certificate of an appropriate officer of the Company;
                  and

                  (ii) an opinion of Latham & Watkins, counsel to the Company.

            (THE REMAINDER OF THIS PAGE IS INTENTIONALLY LEFT BLANK)

<PAGE>   5

         IN WITNESS WHEREOF, the parties hereto have caused this Second
Supplemental Indenture to be duly executed as of the day and year written above.

                                        CHANCELLOR MEDIA CORPORATION
                                        OF LOS ANGELES, as Issuer

                                        /s/ Matthew E. Devine
                                        ----------------------------------------
                                        By: Matthew E. Devine
                                        Title: Senior Vice President
Attest:  /s/
         ---------------------------
         Title:

                                        U.S. TRUST COMPANY OF TEXAS, N.A.,
                                        as Trustee

                                        /s/ Bill Barber
                                        ----------------------------------------
                                        By: Bill Barber
                                        Title:   Vice President
Attest:  /s/
         ---------------------------
         Title: Vice President

                                        KATZ COMMUNICATIONS, INC.,
                                        as Guarantor

                                        /s/ Richard E. Vendig
                                        ----------------------------------------
                                        By: Richard E. Vendig
                                        Title: Senior Vice President, Chief
                                        Financial and Administrative Officer,
                                        Treasurer
Attest:  /s/
         ---------------------------
         Title:

                                        KATZ MILLENNIUM MARKETING INC.,
                                        as Guarantor

                                        /s/ Richard E. Vendig
                                        ----------------------------------------
                                        By: Richard E. Vendig
                                        Title: Senior Vice President, Chief
                                        Financial and Administrative Officer,
                                        Treasurer
Attest:  /s/
         ---------------------------
         Title:

<PAGE>   6

                                        AMCAST RADIO SALES, INC.,
                                        as Guarantor

                                        /s/ Richard E. Vendig
                                        ----------------------------------------
                                        By: Richard E. Vendig
                                        Title: Senior Vice President, Chief
                                        Financial and Administrative Officer,
                                        Treasurer
Attest:  /s/
         ---------------------------
         Title:

                                        CHRISTAL RADIO SALES, INC.,
                                        as Guarantor

                                        /s/ Richard E. Vendig
                                        ----------------------------------------
                                        By: Richard E. Vendig
                                        Title: Senior Vice President, Chief
                                        Financial and Administrative Officer,
                                        Treasurer
Attest:  /s/
         ---------------------------
         Title:

                                        EASTMAN RADIO SALES, INC.,
                                        as Guarantor

                                        /s/ Richard E. Vendig
                                        ----------------------------------------
                                        By: Richard E. Vendig
                                        Title: Senior Vice President, Chief
                                        Financial and Administrative Officer,
                                        Treasurer
Attest:  /s/
         ---------------------------
         Title:

                                        SELTEL INC.,
                                        as Guarantor

                                        /s/ Richard E. Vendig
                                        ----------------------------------------
                                        By: Richard E. Vendig
                                        Title: Senior Vice President, Chief
                                        Financial and Administrative Officer,
                                        Treasurer
Attest:  /s/
         ---------------------------
         Title:

<PAGE>   7

                                        KATZ CABLE CORPORATION,
                                        as Guarantor

                                        /s/ Richard E. Vendig
                                        ----------------------------------------
                                        By: Richard E. Vendig
                                        Title: Senior Vice President, Chief
                                        Financial and Administrative Officer,
                                        Treasurer
Attest:  /s/
         ---------------------------
         Title

                                        THE NATIONAL PAYROLL COMPANY, INC.,
                                        as Guarantor

                                        /s/ Richard E. Vendig
                                        ----------------------------------------
                                        By: Richard E. Vendig
                                        Title: Senior Vice President, Chief
                                        Financial and Administrative Officer,
                                        Treasurer
Attest:  /s/
         ---------------------------
         Title:

                                        KATZ MEDIA CORPORATION
                                        (formerly known as the Cable Company,
                                        Inc.)
                                        as Guarantor

                                        /s/ Richard E. Vendig
                                        ----------------------------------------
                                        By: Richard E. Vendig
                                        Title: Senior Vice President, Chief
                                        Financial and Administrative Officer,
                                        Treasurer
Attest:  /s/
         ---------------------------
         Title:

                                        KATZ MEDIA CORPORATION,
                                        as Guarantor

                                        /s/ Richard E. Vendig
                                        ----------------------------------------
                                        By: Richard E. Vendig
                                        Title: Senior Vice President, Chief
                                        Financial and Administrative Officer,
                                        Treasurer
Attest:  /s/
         ---------------------------
         Title:

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