We have searched for the rare decay W^+/- -> pi^+/- + gamma in 16.7
pb^-1 of data taken in proton-antiproton collisions at sqrt s = 1.8 TeV with
the CDF detector at Fermilab.  We find one event consistent with the expected
signal, and estimate the background to be 2.6 +/- 1.0(stat) +/- 1.3(syst)
events.  Without background subtraction, we find the ratio of partial widths
to be Gamma(W^+/- -> pi^+/- + gamma)/Gamma(W^+/- -> e^+/- + nu) \leq 2.0 x
10^-3 at the 95% confidence level.