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