We report an analysis of the Lambda(0)(b) -> Lambda(+)(c)pi(-)pi(+)pi(-) decay in a data sample collected by the CDF II detector at the Fermilab Tevatron corresponding to 2.4 fb(-1) of integrated luminosity. We reconstruct the currently largest samples of the decay modes Lambda(0)(b) -> Lambda(c)(2595)(+)pi(-) (with Lambda(c)(2595)(+) -> Lambda(+)(c)pi(+)pi(-)), Lambda(0)(b) -> Lambda(c)(2625)(+)pi(-) (with Lambda(c)(2625)(+) -> Lambda(+)(c)pi(+)pi(-)), Lambda(0)(b) -> Sigma(c)(2455)(++)pi(-)pi(-) (with Sigma(c)(2455)(++) -> Lambda(+)(c)pi(+)), and Lambda(0)(b) ->Sigma(c)(2455)(0)pi(+)pi(-) (with Sigma(c)(2455)(0) -> Lambda(+)(c)pi(-)) and measure the branching fractions to the Lambda(0)(b) -> Lambda(+)(c)pi(-) branching fraction. We measure the ration B(Lambda(0)(b) -> Lambda(+)(c)pi(-)pi(+)pi(-))/B(Lambda(0)(b) -> Lambda(+)(c)pi(-)) = 3.04 +/- 0.33(stat)(-0.55)(+0.70)(syst) which is used to derive B(Lambda(0)(b) -> Lambda(+)(c)pi(-)pi(+)pi(-)) = (26.8(-11.2)(+11.9)) x 10(-3). RI Robson, Aidan/G-1087-2011; St.Denis, Richard/C-8997-2012; Prokoshin, Fedor/E-2795-2012; maestro, paolo/E-3280-2010