A highly significant structure is observed in the Λ_{c}^{+}K^{-}π^{+}π^{+} mass spectrum, where the Λ_{c}^{+} baryon is reconstructed in the decay mode pK^{-}π^{+}. The structure is consistent with originating from a weakly decaying particle, identified as the doubly charmed baryon Ξ_{cc}^{++}. The difference between the masses of the Ξ_{cc}^{++} and Λ_{c}^{+} states is measured to be 1334.94±0.72(stat.)±0.27(syst.) MeV/c^{2}, and the Ξ_{cc}^{++} mass is then determined to be 3621.40±0.72(stat.)±0.27(syst.)±0.14(Λ_{c}^{+}) MeV/c^{2}, where the last uncertainty is due to the limited knowledge of the Λ_{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.