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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.
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