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, 2019 (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 26, 2019

/s/ J. Patrick Gallagher, Jr.

J. Patrick Gallagher, Jr.
President and Chief Executive Officer
(principal executive officer)

A signed original of this written statement required by 18 U.S.C. Section 1350 has been provided to Arthur J. Gallagher & Co. and will be retained by Arthur J. Gallagher & Co. and furnished to the Securities Exchange Commission or its staff upon request.