We present a measurement of the top quark pair production cross section in pp collisions at square root of s = 1.96 TeV using 318 pb(-1) of data collected with the Collider Detector at Fermilab. We select tt[over ] decays into the final states enu+jets and mu nu+ 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)(-0.9)+1.1(syst) pb. We also report the first observation of tt[over ] with significance greater than 5sigma in the subsample in which both b quarks are identified, corresponding to a cross section of 10.1(-1.4)+1.6(stat)(-1.3)+2.0(syst) pb.