In a data sample of approximately four million hadronic Z decays recorded with the ALEPH detector from 1990 to 1995, a search for the strange b baryon Ξb is performed with a study of Ξ-lepton correlations. Forty-four events with same sign Ξ−ℓ− combinations are found whereas 8.4 are expected based on the rate of opposite sign Ξ−ℓ+ combinations. This significant excess is interpreted as evidence for Ξb semileptonic decays. The measured product branching ratio is per lepton species, averaged over electrons and muons, with Xc a charmed baryon. The Ξb lifetime is measured to be τΞb = 1.35−0.28+0.37(stat)−0.17+0.15(syst) ps.