  Gluon fragmentation to $\chicJ(1P)$ followed by single photon emission
represents the dominant source of prompt $J/\Psi$'s at the Tevatron for
$p_\perp \gtap 6 \GeV$. Since fragmenting gluons are approximately transverse,
their products are significantly polarized. We find that gluon fragmentation
populates the helicity levels of $\chione$, $\chitwo$ and $J/\Psi$ according to
$D_{\chione^{(h=0)}}: D_{\chione^{(|h|=1)}} \simeq 1:1$, $D_{\chitwo^{(h=0)}} :
D_{\chitwo^{(|h|=1)}} : D_{\chitwo^{(|h|=2)}} \simeq 1:2.9:6.0$ and
$D_{\J^{(h=0)}} : D_{\J^{(|h|=1)}} \simeq 1:3.4$. We also speculate that gluon
fragmentation to the radially excited $\chitwo(2P)$ state followed by
subsequent radiative decay could represent a large source of $\psi'(2S)$'s and
potentially resolve the $\psi'$ deficit problem. A measurement of these states'
polarizations would test this idea.
