Arthur J. Gallagher & Co. (AJG) 10-Q 2005 Q2 Quarterly report

Exhibit 32.1

Section 1350 Certification of Chief Executive Officer

I, J. Patrick Gallagher, Jr., the chief executive officer of Arthur J. Gallagher & Co., certify that (i) the Quarterly Report on Form 10-Q of Arthur J. Gallagher & Co. for the quarterly period ended June 30, 2005 (the “Form 10-Q”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and (ii) the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of Arthur J. Gallagher & Co. and its subsidiaries.

Date: July 28, 2005

/s/ J. Patrick Gallagher, Jr.

J. Patrick Gallagher, Jr.

President and Chief Executive Officer

(principal executive officer)