Using a sample of (470.9 +- 2.8) x 10^6 BB-bar pairs, we measure the decay branching fraction B(B^0 -> D^*- pi^+ pi^- pi^+) = (7.26 +- 0.11 +- 0.31) x 10^-3, where the first uncertainty is statistical and the second is systematic. Our measurement will be helpful in studies of lepton universality by measuring B(B^0 -> D^*- tau^+ nu_tau) using tau^+ -> pi^+ pi^- pi^+ nu-bar_tau decays, normalized to B(B^0 -> D^*- pi^+ pi^- pi^+.