The primordial ingredient of cuprate superconductivity is the CuO₂ unit cell. Here, theoretical attention usually concentrates on the intra-atom Coulombic interactions dominating the 3d⁹ and 3d¹⁰ configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p⁶ orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long predicted intra-unit cell symmetry breaking should then generate an orbital ordered phase, for which the charge-transfer energy ε separating the 2p⁶ and 3d¹⁰ orbitals is distinct for the two oxygen atoms. Here we introduce sublattice resolved ε(r) imaging techniques to CuO₂ studies and discover intra-unit-cell rotational symmetry breaking of ε(r), with energy-level splitting between the two oxygen atoms on the 50 meV scale. Spatially, this state is arranged in Ising domains of orthogonally oriented orbital order that appear bounded by dopant ions, and within whose domain walls low energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q=0 orbitally ordered state that splits the energy levels of the oxygen orbitals by ~50 meV, in CuO₂.