  A search for the lepton-flavor-violating decay of the tau into three charged
leptons has been performed using $91.5 \mathrm{fb}^{-1}$ of data collected at
an $e^+e^-$ center-of-mass energy of 10.58 GeV with the BaBar detector at the
PEP-II storage ring. 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 $(1-3) \times 10^{-7}$ at 90%
confidence level.
