We present a search for the decay B+→τ+ν using 383×106BB̄ pairs collected at the Υ(4S) resonance with the BABAR detector at the SLAC PEP-II B-Factory. A sample of events with one reconstructed semileptonic B decay (B-→D0 -ν̄ X) is selected, and in the recoil a search for B+→τ+ν is performed. The τ is identified in the following channels: τ+→e+νν̄, τ+→μ+νν̄, τ+→π+ν̄, and τ+→π+π0ν̄. We measure a branching fraction of B(B+→τ+ν)=(0.9±0.6(stat.)±0.1(syst.))×10-4. In the absence of a significant signal, we calculate an upper limit at the 90% confidence level of B(B+→τ+ν)<1.7×10-4. We calculate the product of the B meson decay constant fB and |Vub| to be fB•|Vub|=(7.2-2. 8+2.0(stat.)±0.2(syst.))×10-4GeV. © 2007 The American Physical Society.