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Using proton-proton collision data corresponding to an integrated luminosity of 140 fb(-1) collected by the CMS experiment at root s = 13 TeV, the Lambda(0)(b) -> J/psi Xi K--(+) decay is observed for the first time, with a statistical significance exceeding 5 standard deviations. The relative branching fraction, with respect to the Lambda(0)(b) -> psi(2S)Lambda decay, is measured to be B(Lambda(0)(b) -> J/psi Xi K--(+))/B(Lambda(0)(b) -> psi(2S)Lambda) = [3.38 +/- 1.02 +/- 0.61 +/- 0.03]%, where the first uncertainty is statistical, the second is systematic, and the third is related to the uncertainties in B(psi(2S) -> J/psi pi(+)pi(-)) and B(Xi(-) -> Lambda pi(-)).