The first observation of the Cabibbo-suppressed decay Lambda(0)(b) -> J / psi p pi(-) is reported using a data sample of proton-proton collisions at 7 and 8TeV, corresponding to an integrated luminosity of 3 fb(-1). A prominent signal is observed and the branching fraction relative to the decay mode Lambda(0)(b) -> J / psi pK(-) is determined to be B(Lambda(0)(b) -> J / psi p pi(-))/ B(Lambda(0)(b) -> J / psi pK(-)) = 0.0824 +/- 0.0025 (stat) +/- 0.0042 (syst). A search for direct CP violation is performed. The difference in the CP asymmetries between these two decays is found to be ACP(Lambda(0)(b) -> J / psi p pi(-))/ A(CP)(Lambda(0)(b) -> J / psi pK(-)) = (+5.7 +/- 2.4 (stat) +/- 1.2 (syst))%, which is compatible with CP symmetry at the 2.2 sigma level.