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We present a search for the decay B + → τ + ν using 467.8 × 10 6 B ¯¯¯ B pairs collected at the Υ ( 4 S ) resonance with the BABAR detector at the SLAC PEP-II B -Factory. We select a sample of events with one completely reconstructed B − in the hadronic decay mode ( B − → D ( * ) 0 X − and B − → J / ψ X − ). We examine the rest of the event to search for a B + → τ + ν decay. We identify the τ + lepton in the following modes: τ + → e + ν ¯ ν , τ + → μ + ν ¯ ν , τ + → π + ¯ ν and τ + → ρ + ¯ ν . We find an excess of events with respect to the expected background, which excludes the null signal hypothesis at the level of 3.8 σ (including systematic uncertainties) and corresponds to a branching fraction value of B ( B + → τ + ν ) = ( 1.83 + 0.53 − 0.49 ( stat ) ± 0.24 ( syst ) ) × 10 − 4 .