We report a measurement of the tt production cross section using the CDF II detector at the Fermilab Tevatron. The data consist of events with an energetic electron or muon, missing transverse energy, and three or more hadronic jets, at least one of which is identified as a b-quark jet by reconstructing a secondary vertex. The background fraction is determined from a fit of the transverse energy of the leading jet. Using 162±10  pb−1 of data, the total cross section is found to be 6.0±1.6(stat.)±1.2(syst.)  pb, which is consistent with the standard model prediction.