Abstract: The Lambda K-+(c)- mass spectrum is studied with a data sample of pp collisions at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 5.6 fb(-1) collected by the LHCb experiment. Three Xi(0)(c) states are observed with a large significance and their masses and natural widths are measured to be m[Xi(c)(2923)(0)] = 2923.04 +/- 0.25 +/- 0.20 +/- 0.14 MeV, Gamma[Xi(c)(2923)(0)] = 7.1 +/- 0.8 +/- 1.8 MeV, m[Xi(c)(2939)(0)] = 2938.55 +/- 0.21 +/- 0.17 +/- 0.14 MeV, Gamma[Xi(c)(2939)(0)] = 10.2 +/- 0.8 +/- 1.1 MeV, m[Xi(c)(2965)(0)] = 2964.88 +/- 0.26 +/- 0.14 +/- 0.14 MeV, Gamma[Xi(c)(2965)(0)] = 14.1 +/- 0.9 +/- 1.3 MeV, where the uncertainties are statistical, systematic, and due to the limited knowledge of the Lambda(+)(c) mass. The Xi(c)(2923)(0) and Xi(c)(2939)(0) baryons are new states. The Xi(c)(2965)(0) state is in the vicinity of the known Xi(c)(2970)(0) baryon; however, their masses and natural widths differ significantly.