The first observation of the Omega(-)(b) -> Xi(+)(c) K-pi(-) decay is reported using p p collision data at center of mass energies of 7, 8, and 13 TeV collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb(-1). Four excited Omega(0)(c) baryons are observed in the Xi K-+(c)- mass projection of the Omega(-)(b) -> Xi K-+(c)-pi(-) decays with the significance of each exceeding five standard deviations. They coincide with the states previously observed in prompt pp and e(+)e(-) production. Relative production rates, masses, and natural widths of the states are measured, and a test of spin hypotheses is performed. Moreover, the branching ratio of Omega(-)(b) -> Xi K-+(c)-pi(-) is measured relative to the Omega(-)(b) -> Omega(0)(c)pi(-) decay mode and a precise measurement of the Omega(-)(b) mass of 6044.3 +/- 1.2 +/- 1.1(-0.22)(+0.19) MeV is obtained.