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 (CDF).  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.