We present a search for the decay B + → τ + ν using 383 × 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 tag B in a hadronic decay mode ( B − → D ( * ) 0 X − ), and 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 + → π + π 0 ¯ ν . We find a 2.2 σ excess in data and measure a branching fraction of B ( B + → τ + ν ) = ( 1.8 + 0.9 − 0.8 ( stat . ) ± 0.4 ( bkg .   syst . ) ± 0.2 ( other   syst . ) ) × 10 − 4 . We calculate the product of the B meson decay constant f B and | V u b | to be f B ⋅ | V u b | = ( 10.1 + 2.3 − 2.5 ( stat . ) + 1.2 − 1.5 ( syst . ) ) × 10 − 4     GeV .