Abstract: The decay Lambda(0)(b) -> Lambda(+)(c)p (p) over bar pi(-) is observed using pp collision data collected with the LHCb detector at centre-of-mass energies of root s = 7 and 8 Tev, corresponding to an integrated luminosity of 3 fb(-1). The ratio of branching fractions between Lambda(0)(b) -> Lambda(+)(c)p (p) over bar pi(-) and Lambda(0)(b) -> Lambda(+)(c)pi(-) decays is measured to be B(Lambda(0)(b) -> Lambda(+)(c)p (p) over bar pi(-))/B(Lambda(0)(b) -> Lambda(+)(c)pi(-) = 0.0540 +/- 0.0023 +/- 0.0032. Two resonant structures are observed in the Lambda(+)(c)pi(-) mass spectrum of the Lambda(0)(b) -> Lambda(+)(c)pp pi(-) decays, corresponding to the Xc(2455) and X (2520) states. The ratios of branching fractions with respect to the decay Lambda(0)(b) -> Lambda(+)(c)p (p) over bar pi(-) are B(Lambda(0)(b) -> Sigma(0)(c)p (p) over bar x B(Sigma(0)(b) -> Lambda(+)(c)pi(-))/B(Lambda(0)(b) -> Lambda(+)(c)p (p) over bar pi(-)) = 0.089 +/- 0.015 +/- 0.006, B(Lambda(0)(b) -> Sigma(c)*(0)p (p) over bar x B(Sigma(c)*(0) -> Lambda(+)(c)pi(-))/B(Lambda(0)(b) -> Lambda(+)(c)p (p) over bar pi(-)) = 0.119 +/- 0.020 +/- 0.014. In all of the above results, the first uncertainty is statistical and the second is systematic. The phase space is also examined for the presence of dibaryon resonances. No evidence for such resonances is found.