Using a sample of ( 470.9 ± 2.8 ) × 1 0 6     B ¯ B pairs, we measure the decay branching fraction B ( B 0 → D * − π + π − π + ) = ( 7.26 ± 0.11 ± 0.31 ) × 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 * − τ + ν τ ) using τ + → π + π − π + ¯ ν τ decays, normalized to B ( B 0 → D * − π + π − π + ) .