The authors prove the existence of a new type of resonance formation in highly doubly excited atoms and ions. The resonant states represent the quantum analogue of a stable planetary atom configuration discovered recently in classical mechanics. The energies and total decay widths of the resonances are calculated quantum mechanically by solving the full three-body Coulomb problem without any approximation. The resonance energies and the structure of the associated wavefunctions coincide with expectations derived from simple semiclassical models. The authors discuss excitation schemes which should allow an experimental observation of these strongly correlated electron states.