Using about 1.5 million hadronic Z decays recorded with the aleph detector, the lifetime of the b baryons has been measured using two independent data samples. From a maximum likelihood fit to the impact parameter distribution of leptons in 519 Λℓ− combinations containing a b baryon sample of 290 decays, the measured b baryon lifetime is τb—baryon = 1.05−0.11+0.12(stat)±0.09(syst) ps. The lifetime of the Λb0 baryon from a maximum likelihood fit to the proper time distribution of 58 Λc+ℓ− candidates containing a Λb0 sample of 44 decays, is τΛb0 = 1.02−0.18+0.23(stat) ± 0.06(syst) ps.