A fully reconstructed Bc-->J/psipi signal is observed with the D0 detector at the Fermilab Tevatron pp[over] collider using 1.3 fb(-1) of integrated luminosity. The signal consists of 54+/-12 candidates with a significance that exceeds 5 standard deviations, and confirms earlier observations of this decay. The measured mass of the Bc meson is 6300+/-14(stat)+/-5(syst) MeV/c2.