  We present a search for the radiative leptonic decays B+ -> e+ nu gamma and
B+ -> mu+ nu gamma using data collected by the BABAR detector at the PEP-II B
factory. We fully reconstruct the hadronic decay of one of the B mesons in
Upsilon(4S) -> B+B- and then search for evidence of the signal decay within the
rest of the event. This method provides clean kinematic information on the
signal's missing energy and high momentum photon and lepton, and allows for a
model-independent analysis of this decay. Using a data sample of 465 million
B-meson pairs, we obtain sensitivity to branching fractions of the same order
as predicted by the Standard Model. We report a model-independent branching
fraction upper limit of BR(B+ -> l+ nu gamma) < 15.6e-6 (l= e or mu) at the 90%
confidence level.
