We report the observation of the baryonic B-decay B^0 → Λ^+_cpK^- π^+, excluding contributions from the decay B^0 → Λ^+_c ΛK^-. Using a data sample of 467 X 10^6 BB pairs collected with the BABAR detector at the PEP-II storage ring at SLAC, the measured branching fraction is (4:33 ± 0:82_(stat) ± 0:33_(syst) ± 1:13Λ^+_c) X 10^(-5). In addition we find evidence for the resonant decay B^0 → ∑_c (2455)^(++) pK^- and determine its branching fraction to be (1:11 ± 0:30_(stat) ± 0:09_(syst) ± 0:29_Λ^+_c) X 10^(-5). The errors are statistical, systematic, and due to the uncertainty in the Λ^+_c branching fraction. For the resonant decay B^0 → Λ^+_c pK^(*0) we obtain an upper limit of 2:42 X 10^(-5_ at 90% confidence level
