We present a measurement of the top pair production cross section in pp collisions at s√=1.96  TeV. We collect a data sample with an integrated luminosity of 194±11  pb−1 with the CDF II detector at the Fermilab Tevatron. We use an artificial neural network technique to discriminate between top pair production and background processes in a sample of 519 lepton+jets events, which have one isolated energetic charged lepton, large missing transverse energy and at least three energetic jets. We measure the top pair production cross section to be σtt=6.6±1.1±1.5  pb, where the first uncertainty is statistical and the second is systematic.