We have searched for the rare decay W±→π±+γ in 16.7 pb−1 of data taken in proton-antiproton collisions at 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 γ(W±→π±+γ)/γ(W±→e±+ν)≤2.0×10−3 at the 95% confidence level.