  We present a search for the decay B+ --> tau+ nu_tau using 467.8 x 10^6 B
B-bar pairs collected at the Upsilon(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 an hadronic decay mode (B- --> D{(*)0}X- and B- --> J/psi
X-). We examine the rest of the event to search for a B+ --> tau+ nu_tau decay.
We identify the tau+ lepton in the following modes: tau+ --> e+ nu nu, tau+ -->
mu+ nu nu, tau+ --> pi+ nu and tau+ --> rho nu. We find an excess of events
with respect to expected background, which excludes the null signal hypothesis
at the level of 3.3 sigma and can be converted to a branching fraction central
value of B( B+ --> tau+ nu_tau )=( 1.80 +0.57 -0.54 (stat.) +-0.26 (syst.)) x
10^{-4}.
