We search for the rare decay W+- --> gamma pi+- in 4.2pb**(-1) of p anti-p
collisions recorded at the Fermilab Tevatron Collider with the CDF detector.
At the 95% confidence level, we find an upper limit on the partial decay width
to be Gamma(W+- --> gamma pi+-)/Gamma(W+- --> e+- nu) <= 7.5*10**(-3).