Orbital reconstructions and covalent bonding must be considered as important factors in the rational design of oxide heterostructures with engineered physical properties. We have investigated the interface between high-temperature superconducting (Y,Ca)Ba(2)Cu3O7 and metallic La(0.67)Ca(0.33)MnO3 by resonant x-ray spectroscopy. A charge of about -0.2 electron is transferred from Mn to Cu ions across the interface and induces a major reconstruction of the orbital occupation and orbital symmetry in the interfacial CuO2 layers. In particular, the Cu d(3z(2)-r(2)) orbital, which is fully occupied and electronically inactive in the bulk, is partially occupied at the interface. Supported by exact-diagonalization calculations, these data indicate the formation of a strong chemical bond between Cu and Mn atoms across the interface. Orbital reconstructions and associated covalent bonding are thus important factors in determining the physical properties of oxide heterostructures.