The ratio of branching fractions ${cal{R}}(D^{*-})equiv {cal{B}}(B^0 to D^{*-} tau^+ u_{tau})/{cal{B}}(B^0 to D^{*-} mu^+ u_{mu})$ is measured using a data sample of proton-proton collisions collected with the LHCb detector at center-of-mass energies of 7 and 8 Tev, corresponding to an integrated luminosity of 3$~$fb$^{-1}$. For the first time ${cal{R}}(D^{*-})$ is determined using the $tau$ lepton decays with three charged pions in the final state. The $B^0 to D^{*-} tau^+ u_{tau}$ yield is normalized to that of the $B^0to D^{*-} pi^+pi^-pi^+$ mode, providing a measurement of ${cal{B}}(B^0to D^{*-}tau^+ u_{tau})/{cal{B}}(B^0to D^{*-}pi^+pi^-pi^+) = 1.97 pm 0.13 pm 0.18$, where the first uncertainty is statistical and the second systematic. The value of ${cal{B}}(B^0 to D^{*-} tau^+ u_{tau}) = (1.42 pm 0.094 pm 0.129 pm 0.054)% $ is obtained, where the third uncertainty is due to the limited knowledge of the branching fraction of the normalization mode. Using the well-measured branching fraction of the $B^0 to D^{*-} mu^+ u_{mu}$ decay, a value of ${cal{R}}(D^{*-}) = 0.291 pm 0.019 pm 0.026 pm 0.013$ is established, where the third uncertainty is due to the limited knowledge of the branching fractions of the normalization and $B^0to D^{*-}mu^+ u_{mu}$ modes. This measurement is in agreement with the Standard Model prediction and with previous results.
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