  Contributions through second order, $O(\alpha ^2_s)$, in perturbative quantum
chromodynamics are calculated analytically for inclusive associated production
of a prompt photon and a charm quark at large values of transverse momentum in
high energy hadron-hadron collisions. Seven partonic subprocesses contribute at
order $\alpha^2_s$. We find important corrections to the lowest order,
$O(\alpha_s)$, subprocess $c g \rightarrow \gamma c$. We demonstrate to what
extent data from $p +\bar{p}\rightarrow \gamma + c + X$ may serve to measure
the charm quark density in the nucleon.
