We present a measurement of the ttbar production cross section in
ppbar collisions at sqrt s = 1.8 TeV using an integrated luminosity of 109
pb^-1 collected with the Collider Detector at Fermilab.  The measurement uses
ttbar decays into final states which contain one or two high transverse
momentum leptons and multiple jets, and final states, which contain only jets.
Using acceptances appropriate for a top quark mass of 175 GeV/c^2, we find
sigma_ttbar = 7.6^ +1.8 _ -1.5 pb.