The lifetimes of the B^- and B-bar^0 mesons are measured using the
partially reconstructed semileptonic decays B-bar -> D l^- nu-bar X, where D
is either a D^0 or D^*+ meson.  The data were collected by the CDF detector at
the Fermilab Tevatron collider during 1992-1995 and correspond to about 110
pb^-1 of pbar p collisions at sqrt s = 1.8 TeV.  We measure decay lengths and
extract the lifetimes to be tau(B^-) = 1.637 +/- 0.058^+0.045_ -0.043 ps and
tau(B-bar^0) = 1.474 +/- 0.039^+0.052_ -0.051 ps, and the ratio of the
lifetimes to be tau(B^-)/tau(B-bar^0) = 1.110 +/- 0.056^+0.033_ -0.030, where
the first uncertainties are statistical and the second are systematic.