We have measured the fraction J/psi originating from chi_c states
in ppbar collisions at sqrt s = 1.8 TeV in four bins of J/psi P_T.  The
fraction in the inclusive CDF J/psi sample with P_T^j/psi > 4.0 GeV/c and
|eta^j/psi| < 0.6 is f_chi^J/psi = 28.3 \pm 1.6 (stat) \pm 6.8 (syst)%.  We
have also found that directly produced chi_c's are produced in the ratio
sigma(chi_c2)/sigma(chi_c1) + sigma(chi_c2) = 0.47 \pm 0.08(stat) \pm
0.02(syst.)