A search for the neutrinoless, lepton-flavor violating decay of the τ 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)×10^(-8) at 90% confidence level
