We present a search for the radiative leptonic decay B+ -> l+ nu gamma, where l=e,mu, using a data sample of 465 million B-meson pairs collected by the BABAR experiment. In this analysis, we fully reconstruct the hadronic decay of one of the B mesons in Upsilon(4S) -> B+B- decays, then search for evidence of B+ -> l+ nu gamma in the rest of the event. We observe no significant evidence of signal decays and report model-independent branching fraction upper limits of BR(B+ -> e+ nu gamma)<17e-6, BR(B+ -> mu+ nu gamma)< 24e-6, and BR(B+ -> l+ nu gamma)<15.6e-6 (l= e or mu), all at the 90% confidence level. Show Partial Abstract