  We calculate the cross section of inclusive direct J/psi photoproduction at
next-to-leading order within the factorization formalism of nonrelativistic
quantum chromodynamics, for the first time including the full relativistic
corrections due to the intermediate ^1S_0^{[8]}, ^3S_1^{[8]}, and ^3P_J^{[8]}
color-octet states. A comparison of our results to recent H1 data suggests that
the color octet mechanism is indeed realized in J/psi photoproduction, although
the predictivity of our results still suffers from uncertainties in the
color-octet long-distance matrix elements.
