We present a measurement of the top quark pair production cross section in pp collisions at s√=1.96  TeV using 318  pb−1 of data collected with the Collider Detector at Fermilab. We select tt decays into the final states eν+jets and μν+jets, in which at least one b quark from the t-quark decays is identified using a secondary vertex-finding algorithm. Assuming a top quark mass of 178  GeV/c2, we measure a cross section of 8.7±0.9(stat)+1.1−0.9(syst)  pb. We also report the first observation of tt with significance greater than 5σ in the subsample in which both b quarks are identified, corresponding to a cross section of 10.1+1.6−1.4(stat)+2.0−1.3(syst)  pb.