  We study J/psi photoproduction via fragmentation at next-to-leading order in
the QCD-improved parton model, using the nonrelativistic factorization
formalism proposed by Bodwin, Braaten, and Lepage. We consider direct and
resolved photoproduction of prompt J/psi mesons and chi_{cJ} mesons radiatively
decaying to J/psi+gamma, taking into account the formation of both
color-singlet and color-octet c anti-c states. Adopting the values of the
long-distance color-octet matrix elements extracted from fits to prompt-J/psi
data recently taken at the Fermilab Tevatron, we predict that measurements of
J/psi photoproduction at DESY HERA should show a distinctive excess over the
expectation based on the color-singlet model at small values of the
inelasticity variable z. This is complementary to the expected enhancement at z
close to 1 due to the color-octet contribution to photon-gluon fusion.
