A search for CP violation in the Lambda(0)(b) -> p pi(-) pi(+) pi(-) decay is performed using LHCb data corresponding to an integrated luminosity of 6.6 fb(-1) collected in pp collisions at center-of-mass energies of 7, 8 and 13 TeV. The analysis uses both triple product asymmetries and the unbinned energy test method. The highest significances of CP asymmetry are 2.9 standard deviations from triple product asymmetries and 3.0 standard deviations for the energy test method. Once the global p-value is considered, all results are consistent with no CP violation. Parity violation is observed at a significance of 5.5 standard deviations for the triple product asymmetry method and 5.3 standard deviations for the energy test method. The reported deviations are given in regions of phase space.