  We calculate the partonic cross sections for the hadroproduction of polarized
chi_{cJ} mesons using the factorization formalism of nonrelativistic QCD. We
also describe how the polarization is passed on to the J/psi mesons in the
radiative feed-down chi_{cJ} -> J/psi + gamma and in the double-cascade decays
of psi' mesons via chi_{cJ} intermediate states. These represent the missing
ingredients needed to predict the polarization of prompt J/psi mesons at the
Fermilab Tevatron.
