  Data collected with the BABAR detector at the PEP-II asymmetric B Factory at
SLAC are used to study the lifetimes of the B^0 and B^+ mesons. The data sample
consists of 7.4 fb-1 collected near the Y(4S) resonance. B^0 and B^+ mesons are
fully reconstructed in several exclusive hadronic decay modes to charm and
charmonium final states. The B lifetimes are determined from the flight length
difference between the two B mesons which are pair-produced in the Y(4S) decay.
The preliminary measurements of the lifetimes are tau_B0 =
1.506+/-0.052(stat)+/-0.029(syst) ps, tau_B+ =
1.602+/-0.049(stat)+/-0.035(syst) ps, and of their ratio is tau_B+/tau_B0 =
1.065+/-0.044(stat)+/-0.021(syst).
