  A search for the neutrinoless, lepton-flavor violating decay of the tau
lepton into three charged leptons has been performed using an integrated
luminosity of 468 fb^-1 collected with the BABAR detector at the PEP-II
collider. In all six decay modes considered, the numbers of events found in
data are compatible with the background expectations. Upper limits on the
branching fractions are set in the range (1.8-3.3) X 10^-8 at 90% confidence
level.
