Abstract: The ratio of branching fractions R(D*(-)) = B(B-0 -> D*(-) tau(+)nu(tau))/(B-0 -> D*(-) mu(+)nu(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). The tau lepton is reconstructed with three charged pions in the final state. A novel method is used that exploits the different vertex topologies of signal and backgrounds to isolate samples of semitauonic decays of b hadrons with high purity. Using the B-0 -> D*(-) pi(+)pi(-)pi(+) decay as the normalization channel, the ratio B(B-0 -> D*(-) tau(+)nu(tau))/B(B-0 -> D* pi(+)pi(-)pi(+)) is measured to be 1.97 +/- 0.13 +/- 0.18, where the first uncertainty is statistical and the second systematic. An average of branching fraction measurements for the normalization channel is used to derive B(B-0 -> D*(-) tau(+)nu(tau))(_)= (1.42 +/- 0.094 +/- 0.129 +/- 0.054)%, where the third uncertainty is due to the limited knowledge of B(B-0 -> D*(-) pi(+)pi(-)pi(+)). A test of lepton flavor universality is performed using the well- measured branching fraction B(B-0 -> D*(-) mu(+)nu(mu)) to compute R(D*(-))0 = 0.291 +/- 0.019 +/- 0.026 +/- 0.013, where the third uncertainty originates from the uncertainties on B(B-0 -> D*(-) pi(+)pi(-)pi(+)) and B(B-0 -> D*(-) mu(+)nu(mu)) This measurement is in agreement with the Standard Model prediction and with previous measurements.