  In exclusive $J/\psi$ production by polarized photons incident on polarized
protons, a finite polarization asymmetry arises because of $c\bar c$
Fermi-motion and binding-energy effects. The asymmetry depends on the polarized
nonforward gluon distribution of the proton and thus gives information on gluon
polarization in the proton. The analyzing power, however, is rather small.
