We present measurements of the polarization of the J/psi produced in 800-GeV proton interactions with a copper target. Polarization of the J/psi is sensitive to the ccmacr; production and hadronization processes. A longitudinal polarization is observed at large x(F), while at small x(F) the state is produced essentially unpolarized or slightly transversely polarized. No significant variation of the polarization is observed versus p(T).