  Using substantially larger data samples collected by the CLEO III detector,
we report on new measurements of the decays of Upsilon(1S) to charmonium final
states, including J/Psi, psi(2S), and chi_cJ. The latter two are first
observations of these decays. We measure the branching fractions as follows:
B(Y(1S)--> J/Psi+X)=(6.4+-0.4+-0.6)x10^-4, B(Y(1S)--> psi(2S)+X)/B(Y(1S)-->
J/Psi+X)=0.41+-0.11+-0.08, B(Y(1S)--> chi_c1+X)/B(Y(1S)-->
J/Psi+X)=0.35+-0.08+-0.06, B(Y(1S)--> chi_c2+X)/B(Y(1S)-->
J/Psi+X)=0.52+-0.12+-0.09, and B(Y(1S)--> chi_c0+X)/B(Y(1S)--> J/Psi+X)<7.4% at
90% confidence level. We also report on the momentum and angular spectra of
J/Psi's in Upsilon(1S) decay. The results are compared to predictions of the
color octet and color singlet models.
