Community Health Systems (CYH) 10-Q 2004 Q3 Quarterly report

Exhibit Number 32.1

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Community Health Systems, Inc. (the “Company”) on Form 10-Q for the period ending September 30, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Wayne T. Smith, Chairman of the Board, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1)The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

 /s/ Wayne T. Smith

Wayne T. Smith

Chairman of the Board, President and Chief Executive Officer

November 4, 2004

A signed original of this written statement required by Section 906 has been provided to Community Health Systems, Inc. and will be retained by Community Health Systems, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.