  We present a calculation for the photoproduction of $\eta_c$ under the
framework of NRQCD factorization formalism. We find a quite unique feature that
the color-singlet contribution to this process vanishes at not only the leading
order but also the next to leading order perturbative QCD calculations and that
the dominant contribution comes from the color-octet ${}^1S_0^{(8)}$
subprocess. The nonperturbative color-octet matrix element of ${}^1S_0^{(8)}$
of $\eta_c$ is related to that of ${}^3S_1^{(8)}$ of $J/\psi$ by the heavy
quark spin symmetry, and the latter can be determined from the direct
production of $J/\psi$ at large transverse momentum at the Fermilib Tevatron.
We then conclude that the measurement of this process may clarify the existing
conflict between the color-octet prediction and the experimental result on the
$J/\psi$ photoprodution.
