We report on the first observation of the bottom-charm mesons B_c
through 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 observed J/psi l mas distribution yielded 20.4^+_
-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 +/- 0.13 GeV/c^2 and the B^+_c lifetime to be
0.46^+0.18_ -0.16(stat.) +/- 0.03(syst.) ps.  The measured 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).