We present a search for the decay B+→τ+ν using 383×106 BB̄ 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 tag B in a hadronic decay mode (B-→D(*)0X-), 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+νν̄, τ+→μ+νν̄, τ+→π+ν̄, and τ+→π+π0ν̄. We find a 2.2σ excess in data and measure a branching fraction of B(B+→τ+ν)=(1.8-0.8+0.9(stat.) ±0.4(bkg.syst.)±0.2(othersyst.))×10-4. We calculate the product of the B meson decay constant fB and |Vub| to be fB•|Vub|=(10.1-2. 5+2.3(stat.)-1.5+1.2(syst.))×10-4GeV. © 2008 The American Physical Society.