A baryonic decay of the B(c)(+) meson, B(c)(+) → J/ψppπ(+), is observed for the first time, with a significance of 7.3 standard deviations, in pp collision data collected with the LHCb detector and corresponding to an integrated luminosity of 3.0 fb(-1) taken at center-of-mass energies of 7 and 8 TeV. With the B(c)(+) → J/ψπ(+) decay as the normalization channel, the ratio of branching fractions is measured to be B(B(c)(+) → J/ψppπ(+))/B(B(c)(+) → J/ψπ(+)) = 0.143(-0.034)(+0.039)(stat) ± 0.013(syst). The mass of the B(c)(+) meson is determined as M(B(c)(+) = 6274.0 ± 1.8(stat) ± 0.4(syst) MeV/c(2), using the B(c)(+) → J/ψppπ(+) channel.