Using the NRQCD factorization formalism, we calculate the total cross section for the photoproduction of hc mesons. We include color-octet and color-singlet mechanisms as well as next-to-leading order perturbative QCD corrections. The theoretical prediction depends on two nonperturbative matrix elements that are not well determined from existing data on charmonium production. For reasonable values of these matrix elements, the cross section is large enough that the hc may be observable at the E831 experiment and at the DESY HERA experiments.