We have measured the fraction of J/psi mesons originating from
Chi_c meson decays in ppbar collisions at sqrt s = 1.8 TeV.  The fraction, for
P_T^{J/psi} > 4.0 GeV/c and |eta^{J/psi}| < 0.6, not including contributions
from b flavored hadrons, is 29.7% +/- 7.1%(stat) +/- 5.7%(syst).  We have
determined the cross sections for J/psi mesons originating from Chi_c decays
and for directly produced J/psi mesons.  We have found that direct J/psi
production is in excess of the prediction of the color singlet model by the
same factor found for direct psi(2S) production.