This paper presents measurements of the J/psi and psi' production
cross sections in ppbar collisions at sqrt s = 1.8 TeV.  The cross sections
are measured in the kinematic region P_T > 5 GeV/c, |eta| < 0.6 using the
dimuon decay channel.  The fraction of events from B decays is measured and
used to calculate the J/psi and psi' cross sections from B decay.  The
fraction of J/psi events from chi_c decays is also measured and used to
calculate the J/psi cross section from direct production.