The decay Λ 0 b → η c ( 1 S ) p K − is observed for the first time using a data sample of proton-proton collisions, corresponding to an integrated luminosity of 5.5 fb − 1 , collected with the LHCb experiment at a center-of-mass energy of 13 TeV. The branching fraction of the decay is measured, using the Λ 0 b → J / ψ p K − decay as a normalization mode, to be B ( Λ 0 b → η c ( 1 S ) p K − ) = ( 1.06 ± 0.16 ± 0.0 6 + 0.22 − 0.19 ) × 10 − 4 , where the quoted uncertainties are statistical, systematic and due to external inputs, respectively. A study of the η c ( 1 S ) p mass spectrum is performed to search for the P c ( 4312 ) + pentaquark state. No evidence is observed and an upper limit of B ( Λ 0 b → P c ( 4312 ) + K − ) × B ( P c ( 4312 ) + → η c ( 1 S ) p ) B ( Λ 0 b → η c ( 1 S ) p K − ) < 0.24 is obtained at the 95% confidence level.