We search for the rare leptonic decay B^+ → τ^+ν_τ in a sample of 232 × 10^6 BB̅ pairs collected with the BABAR detector at the SLAC PEP-II B-Factory. Signal events are selected by examining the properties of the B meson recoiling against the semileptonic decay B^- → D^9*0)ℓ^-ν̅_ ℓ. We find no evidence for a signal and set an upper limit on the branching fraction of B(B^+ → τ^+ν_τ)<2.8 × 10^9-4) at the 90% confidence level. We combine this result with a previous, statistically independent BABAR search for B+→τ+ντ to give an upper limit of B(B^+ → τ^+ν_τ)<2.6 × 10^(-4) at the 90% confidence level
