Abstract: The ratio of branching fractions R(D*(-)) equivalent to B(B-0 -> D*(-) iota(+)v(iota))/B(B-0 -> D*(-) mu+ v(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). For the first time, R(D*-) is determined using the iota-lepton decays with three charged pions in the final state. The B-0 -> D*(-) iota+ v(iota) yield is normalized to that of the B-0 -> D*(-) pi(+) pi(-) pi(+) mode, providing a measurement B-0 -> D*(-) iota+ v(iota) / B(B-0 -> D*(-) pi(+) pi(-) pi(+)) = 1.97 +/- 0.13 +/- 0.18, where the first uncertainty is statistical and the second systematic. The value of (B-0 -> D*(-) iota+ v(iota)) = (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*(-) mu+ v(mu) 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*(-) mu+ v(mu) modes. This measurement is in agreement with the standard model prediction and with previous results.