The Λ_{c}^{+}K^{-} 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 Ξ_{c}^{0} states are observed with a large significance and their masses and natural widths are measured to be m[Ξ_{c}(2923)^{0}]=2923.04±0.25±0.20±0.14 MeV, Γ[Ξ_{c}(2923)^{0}]=7.1±0.8±1.8 MeV, m[Ξ_{c}(2939)^{0}]=2938.55±0.21±0.17±0.14 MeV, Γ[Ξ_{c}(2939)^{0}]=10.2±0.8±1.1 MeV, m[Ξ_{c}(2965)^{0}]=2964.88±0.26±0.14±0.14 MeV, Γ[Ξ_{c}(2965)^{0}]=14.1±0.9±1.3 MeV, where the uncertainties are statistical, systematic, and due to the limited knowledge of the Λ_{c}^{+} mass. The Ξ_{c}(2923)^{0} and Ξ_{c}(2939)^{0} baryons are new states. The Ξ_{c}(2965)^{0} state is in the vicinity of the known Ξ_{c}(2970)^{0} baryon; however, their masses and natural widths differ significantly.