  Determining how much spin is carried by gluon in a polarized proton is a
fundamental problem which cannot be resolved by completely inclusive deep
inelastic measurements. Hadroproduction of heavy flavors is very sensitive to
the gluon content of hadrons. We show that $\chi_2 (3555)$ production in
polarized proton-proton collisions is a good candidate reaction to address this
challenging question.
