We have used the CLEO-II detector at the Cornell Electron Storage Ring
(CESR) to study the inclusive production of charmonium mesons in a sa
mple of 2.15 million B ($) over bar B events. We find inclusive branch
ing fractions of (1.12+/-0.04+/-0.06)% for B-->J/psi X, (0.34+/-0.04+/
-0.03)% for B-->psi'X, and (0.40+/-0.06+/-0.04)% for B-->chi(c1)X. We
also find some evidence for the inclusive production of chi(c2), and s
et an upper limit for the branching fraction of the inclusive decay B-
->eta(c)] X of 0.9% at 90% confidence level. Momentum spectra for incl
usive J/psi,psi, and chi(c1) production are presented. These measureme
nts are compared to theoretical calculations.