  We present cross sections for the reaction $\mu\bar{\mu}\to H\gamma$ over a
range of $\mu\bar{\mu}$ collider energies. The amplitudes for this process
receive tree level contributions and one-loop contributions, which are of
comparable magnitude. The tree level amplitudes are dominated by helicity
non-flip terms and the one-loop amplitudes are dominated by helicity flip
terms. As a consequence, the interference terms between the tree level and
one-loop contributions are negligible. For a 500 GeV $\mu\bar{\mu}$ collider,
the cross section for $H\gamma$ associated production approaches 0.1 fb.
