  We present a measurement of the top quark pair production cross section in
ppbar collisions at sqrt(s)=1.96 TeV using 318 pb^{-1} of data collected with
the Collider Detector at Fermilab. We select ttbar decays into the final states
e nu + 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/c^2, we measure a cross section of 8.7 +-0.9 (stat)
+1.1-0.9 (syst) pb. We also report the first observation of ttbar with
significance greater than 5 sigma 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.
