Charter Communications 10-Q 2004 Q2 Quarterly report

Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE
OFFICER REGARDING PERIODIC REPORT CONTAINING
FINANCIAL STATEMENTS

     I, Carl E. Vogel, the Chief Executive Officer of Charter Communications Holdings, LLC and Charter Communications Holdings Capital Corporation (collectively, the “Company”) in compliance with 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, hereby certify that, the Company’s Quarterly Report on Form 10-Q for the period ended June 30, 2004 (the “Report”) filed with the Securities and Exchange Commission:

• fully complies with the requirements of Section 15(d) of the Securities Exchange Act of 1934; and

• the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Carl E. Vogel  

Carl E. Vogel 

Chief Executive Officer 
August 13, 2004