Abstract: The branching fraction B(B0→D*−τ+ντ) is measured relative to that of the normalization mode B0→D*−π+π−π+ using hadronic τ+→π+π−π+(π0)¯ντ decays in proton-proton collision data at a center-of-mass energy of 13 TeV collected by the LHCb experiment, corresponding to an integrated luminosity of 2  fb−1. The measured ratio is B(B0→D*−τ+ντ)/B(B0→D*−π+π−π+)=1.70±0.10+0.11−0.10, where the first uncertainty is statistical and the second is related to systematic effects. Using established branching fractions for the B0→D*−π+π−π+ and B0→D*−μ+νμ modes, the lepton universality test R(D*−)≡B(B0→D*−τ+ντ)/B(B0→D*−μ+νμ) is calculated, R(D*−)=0.247±0.015±0.015±0.012, where the third uncertainty is due to the uncertainties on the external branching fractions. This result is consistent with the Standard Model prediction and with previous measurements.