An excess of events containing, in a jet, a same-sign Xi(-/+) - l(-/+) pair as compared to those with an opposite-sign Xi(-/+) - l(-/+) pair has been observed in an analysis of 1.7 million hadronic Z(o) decays collected by the DELPHI detector at LEP between 1991 and 1993 inclusive. The probability for this signal to come from non B-baryon decays is less than 5 x 10(-4). The measured production fraction corresponds to: P(b --> B - baryon) x BR(B - baryon --> Xi(-) l(-) X) = (5.9 +/- 2.1 +/- 1.0) x 10(-4), per lepton species, averaged for electrons and muons and assuming the two channels have an equal contribution. Semileptonic decays of Lambda(b) baryons can account for less than 10% of these events and the major part of the signal has to originate from Xi(b) semileptonic decays, Using the subsample of these events where the Xi(-/+) trajectory has been measured in the Vertex Detector, the lifetime of B-baryons producing a Xi(-/+) in their semileptonic decay final state is found to be: tau(B - baryon --> Xi(-) l(-) X) = 1.5(-0.4)(+0.7) +/- 0.3 ps.