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)ν¯τ 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±0.10-0.10+0.11, 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.