The search continues for nickel oxide-based materials with electronic properties similar to cuprate high-temperature superconductors . The recent discovery of superconductivity in the doped infinite-layer nickelate NdNiO (refs. ) has strengthened these efforts. Here, we use X-ray spectroscopy and density functional theory to show that the electronic structure of LaNiO and NdNiO , while similar to the cuprates, includes significant distinctions. Unlike cuprates, the rare-earth spacer layer in the infinite-layer nickelate supports a weakly interacting three-dimensional 5d metallic state, which hybridizes with a quasi-two-dimensional, strongly correlated state with Formula: see text symmetry in the NiO layers. Thus, the infinite-layer nickelate can be regarded as a sibling of the rare-earth intermetallics , which are well known for heavy fermion behaviour, where the NiO correlated layers play an analogous role to the 4f states in rare-earth heavy fermion compounds. This Kondo- or Anderson-lattice-like 'oxide-intermetallic' replaces the Mott insulator as the reference state from which superconductivity emerges upon doping.