  We search for the rare leptonic decay B+ --> tau+ nu_tau in a sample of
232x10^6 BBbar 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*0 l- nu_lbar. We find
no evidence for a signal and set an upper limit on the branching fraction of
BR(B+ --> tau+ nu_tau) < 2.8x10^{-4} at the 90% confidence level. We combine
this result with a previous, statistically independent BABAR search for B+ -->
tau+ nu_tau to give an upper limit of BR(B+ --> tau+ nu_tau) < 2.6x10^{-4} at
the 90% confidence level.
