  The cross section for photoproduction of an isolated prompt photon in
association with a jet is studied in Next-to-Leading Order. The kinematics are
those appropriate for the DESY $ep$ collider HERA. The effects on the cross
section of various experimental cuts including isolation cuts on the photon is
examined. Comparisons with the ZEUS preliminary data using two parametrizations
of the photon structure function is made, and good agreement is found. The data
is not yet precise enough to make a distinction between various models for the
photon structure function.
