We present a measurement of the top quark pair (t t¯) production cross section (σt t¯) in pp¯ collisions at a center-of-mass energy of 1.96 TeV using 230 pb−1 of data collected by the DØ detector at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), large missing transverse energy, and at least four jets, and extract the t ¯t content of the sample based on the kinematic characteristics of the events. For a top quark mass of 175 GeV, we measure σt ¯t = 6.7+1.4 −1.3(stat)+1.6 −1.1(syst) ±0.4(lumi) pb, in good agreement with the standard model prediction.