  We have measured the polarization of J/Psi and Psi(2S) mesons produced in
p\bar{p} collisions at \sqrt{s} = 1.8 TeV, using data collected at CDF during
1992-95.
  The polarization of promptly produced J/Psi [Psi(2S)] mesons is isolated from
those produced in B-hadron decay, and measured over the kinematic range 4[5.5]
< P_T < 20 GeV/c and |y| < 0.6. For P_T \gessim 12 GeV/c we do not observe
significant polarization in the prompt component.
