The ratio of branching fractions R ( D * − ) ≡ B ( B 0 → D * − τ + ν τ ) / B ( B 0 → D * − μ + ν μ ) 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, R ( D * − ) is determined using the τ -lepton decays with three charged pions in the final state. The B 0 → D * − τ + ν τ yield is normalized to that of the B 0 → D * − π + π − π + mode, providing a measurement of B ( B 0 → D * − τ + ν τ ) / B ( B 0 → D * − π + π − π + ) = 1.97 ± 0.13 ± 0.18 , where the first uncertainty is statistical and the second systematic. The value of B ( B 0 → D * − τ + ν τ ) = ( 1.42 ± 0.094 ± 0.129 ± 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 → D * − μ + ν μ decay, a value of R ( D * − ) = 0.291 ± 0.019 ± 0.026 ± 0.013 is established, where the third uncertainty is due to the limited knowledge of the branching fractions of the normalization and B 0 → D * − μ + ν μ modes. This measurement is in agreement with the standard model prediction and with previous results.