  We report first evidence for a fully reconstructed decay mode of the
B_c^{\pm} meson in the channel B_c^{\pm} \to J/psi \pi^{\pm}, with J/psi \to
mu^+mu^-. The analysis is based on an integrated luminosity of 360 pb$^{-1} in
p\bar{p} collisions at 1.96 TeV center of mass energy collected by the Collider
Detector at Fermilab. We observe 14.6 \pm 4.6 signal events with a background
of 7.1 \pm 0.9 events, and a fit to the J/psi pi^{\pm} mass spectrum yields a
B_c^{\pm} mass of 6285.7 \pm 5.3(stat) \pm 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%.
