We present the results of a five-dimensional resonant amplitude analysis of the Λ c + ->pK - π + system based on 946+/-38 reconstructed decays. These data were produced in 500 GeV/c π - -N interactions by Fermilab experiment E791. We report measurements of the amplitudes for Λ c + decay into nonresonant pK - π + and to pK * 0 (890), Δ + + (1232)K - , and Λ(1520)π + and we comment on other possible resonant enhancements. This is the first complete amplitude analysis of the Λ c + ->pK - π + system. We find that (54.8+/-5.5+/-3.5)% of the decays are nonresonant, (19.5+/-2.6+/-1.8)% of the decays are via the K * 0 resonance, (18.0+/-2.9+/-2.9)% of the decays are via the Δ + + resonance, and (7.7+/-1.8+/-1.1)% of the decays are via the Λ(1520) resonance. We find evidence for an increasingly negative polarization of the Λ c + baryons as a function of p T 2 , in agreement with a recent model [W.G.D. Dharmaratna, G.R. Goldstein, Phys. Rev. D 53 (1996) 1073; G.R. Goldstein, hep-ph/9907573] and with a related measurement [M. Jezabek, K. Rybicki, R. Rylko, Phys. Lett. B 286 (1992) 175].