Abstract: The difference between the CP asymmetries in the decays Lambda(+)(C) -> pK(-)K(+) and Lambda(+)(C) -> p pi(-)pi(+) is presented. Proton-proton collision data taken at centre-of-mass energies of 7 and 8 TeV collected by the LHCb detector in 2011 and 2012 are used, corresponding to an integrated luminosity of 3 fb(-1). The Lambda(+)(C) candidates are reconstructed as part of the Lambda(0)(b) -> Lambda(+)(c)mu X- decay chain. In order to maximize the cancellation of production and detection asymmetries in the difference, the final-state kinematic distributions of the two samples are aligned by applying phase-space-dependent weights to the Lambda(+)(C) -> pK(-)K(+) sample. This alters the definition of the integrated CP asymmetry to A(CP)(wgt)(p pi(-)pi(+)). Both samples are corrected for reconstruction and selection efficiencies across the five-dimensional Lambda(+)(C) decay phase space. The difference in CP asymmetries is found to be Delta A(CP)(wgt) = A(CP)(pK(-)K(+)) – A(CP)(wgt)(p pi(-)pi(+)) = (0.30 +/- 0.91 +/- 0.61) %, where the first uncertainty is statistical and the second is systematic.