  We study the production of neutral scalar (CP even) Higgs bosons in the
process $e\gamma\to e h$ by including supersymmetric corrections to the
dominant $t$-channel photon exchange amplitude. In addition to the standard
model $W^{\pm}$ and fermion loops, there are substantial contributions from
chargino loops. For some cases, these contributions can exceed those of the
$W$'s and ordinary fermions. The cross sections in this channel are generally
one or two orders of magnitude larger than those in the related channel
$e\bar{e}\to\gamma h$.
