We present a search for the decay B+→τ+ν using 467.8×10^6 BB pairs collected at the Υ(4S) 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(*)0X- and B-→J/ψX-). 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+νν , τ+→μ+νν , 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 3.8σ (including systematic uncertainties) and corresponds to a branching fraction value of B(B+→τ+ν)=(1.83_(-0.49)^(+0.53)(stat)±0.24(syst))×10^(-4).
