A search for the lepton flavour violating decay tau(-) -> mu(-)mu(+)mu(-) is performed with the LHCb experiment. The data sample corresponds to an integrated luminosity of 1.0 fb(-1) of proton-proton collisions at a centre-of-mass energy of 7 TeV and 2.0 fb(-1) at 8 TeV. No evidence is found for a signal, and a limit is set at 90% confidence level on the branching fraction, B(tau(-) -> mu(-)mu(+)mu(-)) < 4.6 x 10(-8).