<PAGE>   1
                                                                  EXHIBIT 5.1(a)


                          [VINSON & ELKINS LETTERHEAD]


WRITER'S TELEPHONE                                                 WRITER'S FAX
 (214) 220-7700                                                   (214) 999-7700


                                 August 31, 1998


Capstar Broadcasting Corporation
600 Congress Avenue
Suite 1400
Austin, Texas 78701

Ladies and Gentlemen:

         We have acted as counsel for Capstar Broadcasting Corporation, a
Delaware corporation (the "Company"), in connection with the Company's
registration on Form S-8 under the Securities Act of 1933 (the "Securities Act")
of 2,000,000 shares (the "Shares") of Class A Common Stock, par value $0.01 per
share, of the Company, which may be purchased in the open market and offered
from time to time under the Capstar Broadcasting Partners 401(k) Retirement Plan
and Trust (the "Plan") and of an indeterminate amount of interests in the Plan
under the Company's Registration Statement on Form S-8 (the "Registration
Statement") filed with the Securities and Exchange Commission on August 31,
1998.

         In reaching the opinions set forth herein, we have examined and are
familiar with originals or copies, certified or otherwise identified to our
satisfaction, of such documents and records of the Company and such statutes,
regulations and other instruments as we deemed necessary or advisable for
purposes of this opinion, including (i) the Registration Statement, (ii) the
Amended and Restated Certificate of Incorporation of the Company, as filed with
the Secretary of State of the State of Delaware, (iii) the Bylaws of the
Company, (iv) certain minutes of meetings of, and resolutions adopted by, the
Board of Directors of the Company relating to the Plan, and (v) the Plan.

         We have assumed that (i) all information contained in all documents we
reviewed is true, correct and complete, (ii) all signatures on all documents we
reviewed are genuine, (iii) all documents submitted to us as originals are true
and complete, (iv) all documents submitted to us as copies are true and complete
copies of the originals thereof, and (v) all persons executing and delivering
the documents we examined were competent to execute and deliver such documents.

         Based on the foregoing, and having due regard for the legal
considerations we deem relevant, we are of the opinion that each Share, when
issued pursuant to the terms of the Plan, will be legally issued, fully paid and
non-assessable.



<PAGE>   2
Capstar Broadcasting Corporation
August 31, 1998
Page 2


         This opinion is limited in all respects to the laws of the State of
Texas, the Delaware General Corporation Law and the federal laws of the United
States of America. You should be aware that we are not admitted to the practice
of law in the State of Delaware.

         This opinion letter may be filed as an exhibit to the Registration
Statement. In giving this consent, we do not thereby admit that we come within
the category of persons whose consent is required under Section 7 of the
Securities Act or the rules and regulations of the Securities and Exchange
Commission promulgated thereunder.


                                                          Very truly yours,

                                                          VINSON & ELKINS L.L.P.