  The lifetimes of B+ and B0 mesons are measured using a sample of 150,000
hadronic Z0 decays collected by the SLD experiment at the SLC between 1993 and
1995. The analysis identifies the semileptonic decays of B mesons and
reconstructs the B meson decay length and charge by vertexing the lepton with a
partially reconstructed D meson. This new method results in a sample of 634
(584) charged (neutral) decays with high charge purity. The ratio of B+ : B0
decays in the charged (neutral) sample is 3:1 (1:3). A maximum likelihood fit
yields t(B+) = 1.61 +0.13 -0.12(stat) +/- 0.07(syst) ps, t(B0) = 1.56 +0.14
-0.13(stat) +/- 0.10(syst) ps, and t(B+)/t(B0) = 1.03 +0.16 -0.14(stat) +/-
0.09(syst).
