
<PAGE>   1
 
                                                                   EXHIBIT 23.10
 
                   CONSENT OF INDEPENDENT PUBLIC ACCOUNTANTS
 
The Board of Directors
Evergreen Media Corporation:
 
As independent public accountants, we hereby consent to the incorporation by
reference in this Registration Statement on Form S-4 of Evergreen Media
Corporation of our report dated March 31, 1997 (and to all references to our
Firm) included in Chancellor Broadcasting Company's previously filed Form 8-K
dated May 30, 1997 and filed June 4, 1997.
 
                                            ARTHUR ANDERSEN LLP
 
Washington, D.C.
July 31, 1997
