Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Altria Group, Inc. (the “Company”) on Form 10-Q for the period ended March 31, 2012 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Michael E. Szymanczyk, Chairman and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

/s/ MICHAEL E. SZYMANCZYK                                    

Michael E. Szymanczyk

Chairman and Chief Executive Officer

April 26, 2012

A signed original of this written statement required by Section 906, or other document authenticating, acknowledging, or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Altria Group, Inc. and will be retained by Altria Group, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.

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