Chubb (CHB) 10-K 2012 FY Annual report

Exhibit 32.2

THE CHUBB CORPORATION

CERTIFICATION OF PERIODIC REPORT

I, Richard G. Spiro, Executive Vice President and Chief Financial 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 Annual Report on Form 10-K of the Corporation for the annual period ended December 31, 2012 (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: February 28, 2013

/S/    RICHARD G. SPIRO

Richard G. Spiro

Executive Vice President and Chief Financial Officer