Using a sample of 9.7 X 10(6) B (B) over bar meson pairs collected with the
CLEO detector, we study B decays to the chi (c1) and chi (c2) charmonia st
ates, which are reconstructed via their radiative decays to J/psi. We first
measure the branching fraction for inclusive chi (c1) production in B deca
ys to be B(B --> chi X-c1) = (4.14 +/- 0.31 +/- 0.40) X 10(-3) where the fi
rst uncertainty is statistical and the second one is systematic. We derive
the branching fractions for direct chi (c1) and chi (c2) production in B de
cays by subtracting the known contribution of the decay chain B --> psi (2S
)X with psi (2S)--> chi (c1,2)gamma. We obtain B[B --> chi (c1) (direct)X]
=(3.83 +/- 0.31 +/- 0.40) X 10(-3). No statistically significant signal for
chi (c2) production is observed in either case. Using the Feldman-Cousins
approach, we determine the 95% confidence intervals to be [0.2.2.0] X 10(-3
) for B(B --> chi X-c2). [0.0,1.7] X 10(-3) for B[B --> chi (c2) (direct)X]
, and [0.00,0.44] for the ratio Gamma [B --> chi (c2) (direct)X-y]/Gamma [B
--> chi (c1) (direct)X-s]. We also measure the branching ratio Gamma [B --
> chi (c2) (direct)X-y]/Gamma [B --> chi (c1) (direct)X-s] for different X-
s configurations by reconstructing B decays into exclusive final states wit
h J/psi, gamma, a kaon, and up to four pions. For all the X-s configuration
s, we observe a strong chi (c1) signal yet no statistically significant chi
(c2) signal. We discuss how our results compare with theoretical predictio
ns in different models of charmonium production.