We present results of a search for the decays B 0 → ℓ + ℓ − γ ( ℓ = e or μ ). The search is performed using 320 × 10 6 B ¯¯¯ B pairs collected at the Υ ( 4 S ) resonance with the BABAR detector at the PEP-II B Factory at SLAC. We find no significant signal and set the following branching fraction upper limits at the 90% confidence level: B ( B 0 → e + e − γ ) < 1.2 × 10 − 7 and B ( B 0 → μ + μ − γ ) < 1.6 × 10 − 7