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The decay B 0 → Λ c + Λ ¯ c − K S 0 is studied at LHCb for the first time using proton-proton collision data recorded by the LHCb experiment at a center-of-mass energy of s = 13 TeV , corresponding to an integrated luminosity of 5.4 fb − 1 . The branching ratio relative to the decay B + → Λ c + Λ ¯ c − K + is measured to be [ B ( B 0 → Λ c + Λ ¯ c − K S 0 ) ] / [ B ( B + → Λ c + Λ ¯ c − K + ) ] = 0.53 ± 0.05 ± 0.05 where the first uncertainty is statistical and the second is systematic. Evidence is found for contributions from two resonant states, Ξ c ( 2923 ) + and Ξ c ( 2939 ) + , in the Λ c + K S 0 system. The two states show a significance of 3.9 σ relative to the nonresonant hypothesis. These two Ξ c + states are consistent with being the isospin partners of the states observed in the Λ c + K − system.