We present the results of a search for B{sup +} meson decays into {gamma}{ell}{sup +}{nu}{sub {ell}}, where {ell} = e,{mu}. We use a sample of 232 million B{bar B} meson pairs recorded at the {Upsilon}(4S) resonance with the BABAR detector at the PEP-II B factory. We measure a partial branching fraction {Delta}{beta} in a restricted region of phase space that reduces the effect of theoretical uncertainties, requiring the lepton energy to be in the range 1.875 and 2.850 GeV, the photon energy to be in the range 0.45 and 2.35 GeV, and the cosine of the angle between the lepton and photon momenta to be less than -0.36, with all quantities computed in the {Upsilon}(4S) center-of-mass frame. We find {Delta}{Beta}(B{sup +} {yields} {gamma}{ell}{sup +}{nu}{sub {ell}}) = (-0.3{sub 1.5}{sup +1.3}(statistical){sub -0.6}{sup +0.6}(systematic) {+-} 0.1(theoretical)) x 10{sup -6}, under the assumption of lepton universality. Interpreted as a 90% confidence-level Bayesian upper limit, the result corresponds to 1.7 x 10{sup -6} for a prior at in amplitude, and 2.3 x 10{sup -6} for a prior at in branching fraction.