  We have searched for neutrinoless tau lepton decays into three charged
leptons using an 87.1 fb^{-1} data sample collected with the Belle detector at
the KEKB e^+e^- collider. Since the number of signal candidate events is
compatible with that expected from the background, we set 90% confidence level
upper limits on the branching fractions in the range (1.9-3.5) x 10^{-7} for
various decay modes tau -> l l l where l represents e or mu.
