Title: Measurement of the B+ and B0 Lifetimes using Topological Vertexing at SLD Abstract: The lifetimes of B+ and B0 mesons have been measured using the entire sample of polarized Z0 decays collected by the SLD experiment between 1993 and 1998. We report the inclusive analysis of the 400,000 hadronic Z0's collected between 1996 and 1998 using the upgraded vertex detector (VXD3). Approximately 50,000 B hadron decay vertices are reconstructed with good charge purity. This charge purity is then enhanced using vertex information, as well as information on the initial state flavor of the hemisphere containing the vertex. Combining these results with the previously published 1993-95 SLD results (based upon the 150,00 hadronic Z0's obtaining using the VXD2 vertex detector), we obtain individual meson lifetimes with total errors between 2 and 3%, and a total error on the lifetime ratio of approximately 3.5%.