
<PAGE>
 
                                                                    Exhibit 23.1



                      CONSENT OF INDEPENDENT ACCOUNTANTS
                      ----------------------------------

We hereby consent to the incorporation by reference in the Prospectus 
constituting part of the Registration Statement on Form S-3 (No. 33-93874) of 
Evergreen Media Corporation and in the Registration Statements on Form S-8 (Nos.
333-04379 and 33-83124) of Evergreen Media Corporation of our report dated 
August 22, 1996 relating to the financial statements of Century Chicago 
Broadcasting, L.P. as of December 31, 1995 and for the year then ended, which 
appears in the Current Report on Form 8-K of Evergreen Media Corporation dated 
September 20, 1996.



PRICE WATERHOUSE LLP

Chicago, Illinois
September 20, 1996
