  Using a sample of 9.7 million B meson pairs collected with the CLEO detector,
we study inclusive B meson decays to the chi_c1 and chi_c2 charmonia states. We
measure the branching fraction for the inclusive chi_c1 production in B decays
to be Br(B->chi_c1 X)=(4.14+-0.31+-0.40)*10^-3, where the first uncertainty is
statistical and the second one is systematic. We obtain the branching fractions
for direct chi_c1 and chi_c2 production in B decays by subtracting the
contribution from the decay chain B->psi(2S)X with psi(2S)->chi_c1,2 gamma. We
measure Br(B->chi_c1[direct] X)=(3.83+-0.31+-0.40)*10^-3. No statistically
significant signal for chi_c2 production is observed in either case. We
determine the 95% C.L. upper limits to be Br(B->chi_c2 X)<2.0*10^-3,
Br(B->chi_c2[direct] X)<1.7*10^-3, and Br(B->chi_c2[direct]
X)/Br(B->chi_c1[direct] X)<0.44. All quoted results are preliminary.
