The lifetimes of the B^- and Bbar^0 mesons are measured using the
partially reconstructed semileptonic decays Bbar -> Dl^- 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 1992-1993 and correspond to 19.3 pb^-1
of pbar p collisions at sqrt s = 1.8 TeV.  We measure the decay length
distributions and find the lifetimes to be tau(B^-) = 1.56 +/- 0.13 +/- 0.06
ps and tau(Bbar^0) = 1.01 +/- 0.11 +/- 0.02, where the first uncertainties are
statistical and the second are systematic.