The ratio of branching fractions R(D*−)≡B(B0→D*−τ+ντ)/B(B0→D*−μ+νμ) 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 B0→D*−τ+ντ yield is normalized to that of the B0→D*−π+π−π+ mode, providing a measurement of B(B0→D*−τ+ντ)/B(B0→D*−π+π−π+)=1.97±0.13±0.18, where the first uncertainty is statistical and the second systematic. The value of B(B0→D*−τ+ντ)=(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 B0→D*−μ+νμ 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 B0→D*−μ+νμ modes. This measurement is in agreement with the standard model prediction and with previous results.Received 8 November 2017Revised 5 March 2018DOI:https://doi.org/10.1103/PhysRevLett.120.171802Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.© 2018 CERN, for the LHCb CollaborationPhysics Subject Headings (PhySH)Research AreasBranching fractionElectroweak interactionLeptonic, semileptonic & radiative decaysParticles & Fields