Chubb (CHB) 10-Q 2015 Q3 Quarterly report

Exhibit 32.1

THE CHUBB CORPORATION

CERTIFICATION OF PERIODIC REPORT

I, John D. Finnegan, Chairman, President and Chief Executive Officer of The Chubb Corporation (the “Corporation”), certify, pursuant to 18 U.S.C. Section 1350 adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) the Quarterly Report onForm 10-Q of the Corporation for the quarterly period ended September 30, 2015 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and

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

Dated: November 6, 2015

/s/    John D. Finnegan

John D. Finnegan

Chairman, President and Chief Executive Officer