sing about 4 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 1085 Lambda-lepton combinations containing a b baryon sample of 719 decays the measured b baryon lifetime is \tau = 1.18 \pm 0.08(stat) \pm 0.07 (syst) ps The lifetime of the Lambda_b baryon from a maximum likelihood fit to the proper time distribution of 193 Lambda_c-lepton candidates is \tau_{\Lambda_b} = 1.21^{+0.13}_{-0.12}{stat}) \pm 0.04 {syst} ps. The combined result of the two measurements yields an averaged value \tau_{\Lambda_b} = 1.19 \pm{0.0
