We have measured the cross section of gamma + D^*+/- production
in pbar p collisions at sqrt s = 1.8 TeV using the Collider Detector at
Fermilab.  In this kinematic region, the Compton scattering process (g_c ->
gamma_c) is expected to dominate and thus provide a direct link to the charm
quark density in the proton.  From the 45 +/- 18 gamma + D^*+/- candidates
in a 16.4 pb^-1 data sample, we have determined the production cross section
to be 0.38 +/- 0.15(stat) +/- 0.11(syst) nb for the rapidity range
|y(D^*+/-)| < 1.2 and |y(gamma)| < 0.9, and for the transverse momentum range
p_T(D^*+/-) > 6 GeV/c and 16 < p_T(gamma) < 40 GeV/c.  The measured cross
section is compared to a theoretical prediction.