  We calculate the decay rates of $B$ mesons into P-wave charmonium states
using new factorization formulas that are valid to leading order in the
relative velocity of the charmed quark and antiquark and to all orders in the
running coupling constant of QCD. We express the production rates for all four
P states in terms of two nonperturbative parameters, the derivative of the
wavefunction at the origin and another parameter related to the probability for
a charmed-quark-antiquark pair in a color-octet S-wave state to radiate a soft
gluon and form a P-wave bound state. Using existing data on $B$ meson decays
into $\chi_{c1}$ to estimate the color-octet parameter, we find that the
color-octet mechanism may account for a significant fraction of the $\chi_{c1}$
production rate and that $B$ mesons should decay into $\chi_{c2}$ at a similar
rate.
