Exhibit 32.1

THE TRAVELERS COMPANIES, INC.

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED

PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to Rule 13a-14(b) of the Securities Exchange Act of 1934 (the "Exchange Act") and 18 U.S.C. Section 1350, the undersigned officer of The Travelers Companies, Inc. (the "Company") hereby certifies that the Company's Annual Report on Form 10-K for the year ended December 31, 2019 (the "Report") fully complies with the requirements of Section 13(a) or 15(d) of the Exchange Act and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: February 13, 2020	By:	/s/ ALAN D. SCHNITZER
		Name: Alan D. Schnitzer Title: Chairman and Chief Executive Officer

1