  We calculate the cross section for inclusive prompt photon production in
$\gamma\gamma$ collisions, i.e. the reaction $e^+e^-\to \gamma \gamma \to
\gamma X$, in next-to-leading order QCD. We show that at LEP2 energies this
cross section is measurable and is sensitive to the gluon distribution of the
photon, $g^{\gamma}$, which is currently very poorly constrained by data.
