A baryonic decay of the B-c(+) meson, B-c(+) -> J/psi p (p) over bar pi(+) 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/psi pi(+) decay as the normalization channel, the ratio of branching fractions is measured to be B(B-c(+) -> J/psi p (p) over bar pi(+)) /B(B-c(+) -> J/psi pi(+)) = 0.143(-0.034)(+0.039) (stat) +/- 0.013 (syst). The mass of the B-c(+) messon is determined as M(B-c(+)) = 6274.0 +/- 0.4 (sysst) MeV/c(2), using the B-c(+) -> J/psi p (p) over bar pi(+) channel.