A highly significant structure is observed in the Lambda K-+(c)-pi(+)pi(+) mass spectrum, where the Lambda(+)(c) baryon is reconstructed in the decay mode pK(-)pi(+). The structure is consistent with originating from a weakly decaying particle, identified as the doubly charmed baryon Xi(++)(cc). The difference between the masses of the Xi(++)(cc) and Lambda(+)(c) states is measured to be 1334.94 +/- 0.72(stat.) +/- 0.27(syst.) MeV/c(2), and the Xi(++)(cc) mass is then determined to be 3621.40 +/- 0.72(stat.) +/- 0.27(syst.) +/- 0.14(Lambda(+)(c)) MeV/c(2), where the last uncertainty is due to the limited knowledge of the Lambda(+)(c) mass. The state is observed in a sample of proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 1.7 fb(-1), and confirmed in an additional sample of data collected at 8 TeV.