  The fragmentation functions for gluons to split into P-wave heavy quarkonium
states are calculated to leading order in the QCD coupling constant.
Long-distance effects are factored into two nonperturbative parameters: the
derivative of the radial wavefunction at the origin and a second parameter
related to the probability for a heavy-quark-antiquark pair that is produced in
a color-octet S-wave state to form a color-singlet P-wave bound state. The
fragmentation probabilities for a high transverse momentum gluon to split into
the P-wave charmonium states $\chi_{c0}$, $\chi_{c1}$, and $\chi_{c2}$ are
estimated to be $0.4 \times 10^{-4}$, $1.8 \times 10^{-4}$, and $2.4 \times
10^{-4}$, respectively. This fragmentation process may account for a
significant fraction of the rate for the inclusive production of $\chi_{cJ}$ at
large transverse momentum in $p \bar p$ colliders.
