  We consider the production and decay of the $\chi_2$ charmonium state in
polarized and unpolarized $pp$ collisions at RHIC in the framework of an
effective theory based on the QCD multipole expansion. We find that the angular
distribution in the decay of the produced charmonium, $\chi_2 \to J/\psi +
\gamma$, in the unpolarized case allows us to distinguish clearly between the
color singlet and color octet production mechanisms. Once the production
mechanism is known, the angular distribution in the polarized case can be used
to measure the polarized gluon distribution in the proton, $\Delta G(x)$.
