We have observed bottom-charm mesons via the decay mode B^+/-_c ->
J/psi l^+/- nu in 1.8 TeV ppbar collisions using the CDF detector at the
Fermilab Tevatron.  A fit of background and signal contributions to the J/psi
l mass distribution yielded 20.4^+6.2_-5.5 events from B_c mesons.  A fit to
the same distribution with background alone was rejected at the level of 4.8
standard deviations.  We measured the B^+_c mass to be 6.40 +/-
0.39(stat.)+/-0.13(syst.) GeV/c^2 and the B^+_c lifetime to be
0.46^+0.18_-0.16(stat.) +/-0.03(syst.)ps.  Our measured yield (production
cross section times branching ratio) for B^+_c -> J/psi l^+ nu relative to
that for B^+ -> J/psi K^+ is 0.132^+0.041_-0.037(stat.) +/-
0.031(syst.)^+0.032_-0.020(lifetime).