We have searched for the decays B{r_arrow}{mu}{bar {nu}}{sub {mu}}{gamma} and B{r_arrow}e{bar {nu}}{sub e}{gamma} in a sample of 2.7{times}10{sup 6} charged B decays collected with the CLEO II detector. In the muon channel, we observe no candidates in the signal region and set an upper limit on the branching fraction of B(B{r_arrow}{mu}{bar {nu}}{sub {mu}}{gamma}){lt}5.2{times}10{sup {minus}5} at the 90{percent} confidence level. In the electron channel, we observe five candidates in the signal region and set an upper limit on the branching fraction of B(B{r_arrow}e{bar {nu}}{sub e}{gamma}){lt}2.0{times}10{sup {minus}4} at the 90{percent} confidence level. {copyright} {ital 1997} {ital The American Physical Society}