The Bc+/- meson is observed through the decay Bc+/--->J/psipi+/-, in data corresponding to an integrated luminosity of 2.4 fb(-1) recorded by the Collider Detector at Fermilab II detector at the Fermilab Tevatron. A signal of 108+/-15 candidates is observed, with a significance that exceeds 8sigma. The mass of the Bc+/- meson is measured to be 6275.6+/-2.9(stat)+/-2.5(syst) MeV/c2.