We report the first evidence for a fully reconstructed decay mode of the B-c(+/-) meson in the channel B-c(+/-)-\u3e J/psi pi(+/-), with J/psi -\u3emu(+)mu(-). The analysis is based on an integrated luminosity of 360 pb(-1) in p (p) over bar collisions at 1.96 TeV center of mass energy collected by the Collider Detector at Fermilab. We observe 14.6 +/- 4.6 signal events with a background of 7.1 +/- 0.9 events, and a fit to the J/psi pi(+/-) mass spectrum yields a B-c(+/-) mass of 6285.7 +/- 5.3(stat)+/- 1.2(syst) MeV/c(2). The probability of a peak of this magnitude occurring by random fluctuation in the search region is estimated as 0.012%
