In 451 000 hadronic Z0 decays, recorded with the ALEPH detector at LEP, the yields of Λℓ− and Λℓ+ combinations are measured. Semileptonic decays of b baryons result in a signal of 122± 18 (stat.)−23+22 (syst.) Λℓ− combinations. From a fit to the impact parameter distributions of the leptons in the Λℓ− sample, the lifetime of b baryons is measured to be 1.12−0.29+0.32 (stat.) ±0.16 (syst.) ps.