  The polarization of prompt J/psi at the Tevatron is calculated within the
nonrelativistic QCD (NRQCD) factorization framework. The contribution from
radiative decays of P-wave charmonium states decreases, but does not eliminate,
the transverse polarization at large transverse momentum. The prediction agrees
with measurements from the CDF collaboration at intermediate values of p_T, but
disagrees at the large values of p_T measured.
