Abstract: The Lambda(0)(b) -> Lambda+cK+K-pi(-) decay is observed for the first time using a data sample of proton-proton collisions at centre-of-mass energies of root s = 7 and 8 TeV collected by the LHCb detector, corresponding to an integrated luminosity of 3fb(-1). The ratio of branching fractions between the Lambda(0)(b) -> Lambda K-+(c)+ K-pi(-) and the Lambda(0)(b) -> Lambda D-+(c)s(-) decays is measured to be B(Lambda(0)(b) -> Lambda+cK+K-pi(-))/B(Lambda(0)(b) -> Lambda D-+(c)s(-)) = (9.26 +/- 0.29 +/- 0.46 +/- 0.26) x 10(-2), where the first uncertainty is statistical, the second systematic and the third is due to the knowledge of the D-s(-) -> K+K-pi(-) branching fraction. No structure on the invariant mass distribution of the Lambda K-+(c)+ system is found, consistent with no open-charm pentaquark signature.