We present a search for the radiative leptonic decay B+→≤+ v≤ γ, where ≤=e, μ, using a data sample of 465×106 BB̄ pairs collected by the BABAR experiment. In this analysis, we fully reconstruct the hadronic decay of one of the B mesons in Υ(4S)→B+B- decays, then search for evidence of B+→≤+ν≤γ in the rest of the event. We observe no significant evidence of signal decays and report model-independent branching fraction upper limits of B(B+→e+νeγ)<17×10-6, B(B+→μ+νμγ)<24×10-6, and B(B+→e+νeγ) <15.6×10-6 (≤=e or μ), all at the 90% confidence level. © 2009 The American Physical Society.