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 Br(b -> Ξb) × Br(Ξb -> XcXL-overlineνl) × Br(Xc -> Ξ-X') = (5.4+/-1.1 (stat) +/- 0.8 (syst)) × 10-4 per lepton species, averaged over electrons and muons, with Xc a charmed baryon. The Ξb lifetime is measured to be τΞb = 1.35+0.37-0.28 (syat)+0.15-0.17 (syst) ps.
