<PAGE>   1
                                                                    EXHIBIT 4.8

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                     CHANCELLOR RADIO BROADCASTING COMPANY,

                                   as Issuer

                   CHANCELLOR BROADCASTING LICENSEE COMPANY,
                         TREFOIL COMMUNICATIONS, INC.,
                          SHAMROCK BROADCASTING, INC.,
                         SHAMROCK RADIO LICENSES, INC.,
                                      and
                     SHAMROCK BROADCASTING OF TEXAS, INC.,

                                 as Guarantors

                                      AND

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

                                   as Trustee

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

                         SECOND SUPPLEMENTAL INDENTURE

                           Dated as of April 15, 1997

                                       to

                                   Indenture

                         Dated as of February 14, 1996

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

                                  $200,000,000

                        9-3/8% Senior Subordinated Notes

                                    due 2004



================================================================================
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         SECOND SUPPLEMENTAL INDENTURE dated as of April 15, 1997, among
CHANCELLOR RADIO BROADCASTING COMPANY, a Delaware corporation (the "Company"),
TREFOIL COMMUNICATIONS, INC., a Delaware corporation, SHAMROCK BROADCASTING,
INC., a Delaware corporation, SHAMROCK RADIO LICENSES, INC., a Delaware
corporation, SHAMROCK BROADCASTING OF TEXAS, INC., a Texas corporation, and
CHANCELLOR BROADCASTING LICENSEE COMPANY, a Delaware corporation (collectively,
the "Guarantors"), and U.S. TRUST COMPANY OF TEXAS, N.A., a national banking
association, as Trustee (the "Trustee").

         WHEREAS, the Company and the Guarantors 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 (the
"Indenture") providing for the issuance of $200,000,000 aggregate principal
amount of the Company's 9-3/8% Senior Subordinated Notes due 2004 (the
"Securities");

         WHEREAS, the Company, the Guarantors and the Trustee desire by this
Second Supplemental Indenture, pursuant to and as contemplated by Section 9.02
of the Indenture, to amend certain provisions therein;

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

         WHEREAS, the Company has requested that the holders of the Securities
consent to and approve the amendment set forth herein;

         WHEREAS, the Company has received written consents to such amendment
from holders of at least a majority in aggregate principal amount of the
Securities outstanding; and

         WHEREAS, all conditions and requirements necessary to make this Second
Supplemental Indenture a valid, binding and 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 Securities, as follows:





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                                  ARTICLE ONE

                                   AMENDMENTS

                  Section 1.01. Limitation on Incurrence of Additional
Indebtedness. Section 4.12 of the Indenture is hereby amended and restated in
its entirety to read as follows:

         Section 4.12.  Limitation on Incurrence of Additional Indebtedness.

                  Neither the Company nor any of its Subsidiaries will,
         directly or indirectly, create, incur, assume, guarantee, acquire or
         become liable for, contingently or otherwise, (collectively "incur")
         any Indebtedness other than Permitted Indebtedness. Notwithstanding
         the foregoing limitations, the Company or any Subsidiary may incur
         Indebtedness if on the date of the incurrence of such Indebtedness,
         after giving effect to the incurrence of such Indebtedness and the
         receipt and application of proceeds thereof, the Company's Leverage
         Ratio is less than 7.0 to 1.

                                  ARTICLE TWO

                            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 Securities 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






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Guarantor in this Second Supplemental Indenture and the Securities 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 Securities 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.

                  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
only upon 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
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 Guarantors by corporate
action or otherwise, (iii) the due execution hereof by the Company and the
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.




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         Section 2.08. Effectiveness. This Second Supplemental Indenture shall
become effective once executed upon receipt by the Trustee of a certificate of
an appropriate officer of the Company, substantially in the form of Exhibit A
hereto, dated no earlier than the date hereof.


            [THE REMAINDER OF THIS PAGE IS INTENTIONALLY LEFT BLANK]



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


                                    CHANCELLOR RADIO 
                                    BROADCASTING COMPANY, as Issuer



                                    By:  /s/ J D Kerrest
                                       -------------------------------------
                                         Title: Senior VP and CFO



                                    CHANCELLOR BROADCASTING 
                                    LICENSEE COMPANY, as Guarantor



                                    By:  /s/ J D Kerrest
                                       -------------------------------------
                                         Title:Senior VP and CFO



                                    TREFOIL COMMUNICATIONS, INC., 
                                    as Guarantor



                                    By:  /s/ J D Kerrest
                                       -------------------------------------
                                         Title: Senior VP and CFO



<PAGE>   7

                                   SHAMROCK BROADCASTING, INC., as 
                                   Guarantor



                                   By:  /s/ J D Kerrest
                                       -------------------------------------
                                            Title: Senior VP and CFO



                                   SHAMROCK RADIO LICENSES, INC., 
                                   as Guarantor



                                   By:  /s/ J D Kerrest
                                       -------------------------------------
                                           Title: Senior VP and CFO



                                   SHAMROCK BROADCASTING OF 
                                   TEXAS, INC., as Guarantor



                                   By:  /s/  J D Kerrest
                                       -------------------------------------
                                           Title: Senior VP and CFO



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



                                   By:  /s/ John Stohlmann
                                       -------------------------------------
                                            Title: Vice President




<PAGE>   8
                                                                      EXHIBIT A

                     CHANCELLOR RADIO BROADCASTING COMPANY

                             OFFICERS' CERTIFICATE


         The undersigned each hereby certifies that he is the duly elected,
qualified, and serving President and Senior Vice President, respectively, of
Chancellor Radio Broadcasting Company, a Delaware corporation (the "Company"),
and, in each of their respective capacities as such officer only, hereby
certify on behalf of the Company, and not individually, that:


         1. The undersigned has read Section 9.02 of that certain Indenture,
dated as of February 14, 1996, as amended (the "Indenture"), among the Company,
and Chancellor Broadcasting Licensee Company, Trefoil Communications, Inc.,
Shamrock Broadcasting, Inc., Shamrock Radio Licenses, Inc., and Shamrock
Broadcasting of Texas, Inc., as guarantors, and U.S. Trust Company of Texas,
N.A., as trustee (the "Trustee").

         2. The undersigned has examined the report (a copy of which is
attached hereto as Exhibit A) of Bankers Trust Company, the Company's agent
(the "Agent") with respect to the Company's solicitation of consents of the
holders of its 9-3/8% Senior Subordinated Notes due 2004 (the "Notes") to a
proposed amendment (the "Proposed Amendment") to the Indenture, which report
sets forth the aggregate principal amount of Notes for which valid consents to
the Proposed Amendment have been delivered to the Agent, and not revoked as of
date hereof.

         3. In the undersigned's opinion, the examination and investigation
reasonably necessary to be performed by the undersigned to enable such person
to express an informed opinion as to the matters set forth in this certificate
have been made.

         4. In the undersigned's opinion, all of the conditions and
requirements set forth in Section 9.02 of the Indenture with respect to the
execution, delivery and validity of the Second Supplemental Indenture to the
Indenture, which sets forth the Proposed Amendment have been performed and
fulfilled.


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         IN WITNESS WHEREOF, the undersigned have executed this certificate on
behalf of the Company this ___ day of April __, 1997.


                                                     -------------------------
                                                     Steven Dinetz
                                                     President



                                                     -------------------------
                                                     Jacques D. Kerrest
                                                     Senior Vice President