We present a measurement of the top quark pair (t t¯) production cross section (σt t¯) in pp¯ collisions at √s = 1.96 TeV using 230 pb−1 of data collected by the DØ experiment at the Fermilab Tevatron Collider. We select events with one charged lepton (electron ormuon),missing transverse energy, and jets in the final state.We employ lifetime-based b-jet identification techniques to further enhance the t ¯t purity of the selected sample. For a top quark mass of 175 GeV, we measure σt ¯t = 8.6+1.6 −1.5(stat. + syst.) ±0.6(lumi.) pb, in agreement with the standard model expectation.