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We present a measurement of the tt̅ production cross section using events with one charged lepton and jets from pp̅ collisions at a center-of-mass energy of 1.96 TeV. In these events, heavy flavor quarks from top quark decay are identified with a secondary vertex tagging algorithm. From 162 pb-1 of data collected by the Collider Detector at Fermilab, a total of 48 candidate events are selected, where 13.5±1.8 events are expected from background contributions. We measure a tt̅ production cross section of 5.6-1.1+1.2 (stat.) -0.6+0.9 (syst.) pb.