Polarized J/psi from chi_(cJ) and psi' Decays at the Tevatron

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.