We present a measurement of the ttbar production cross section using events with one charged lepton and jets from ppbar 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 ttbar production cross section of 5.6^{+1.2}_{-1.1} (stat.) ^{+0.9}_{0.6} (syst.) pb.
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