Last date for submission of paper: unknown; Contact person: unknown; We construct quantum error-correcting codes that embed a finite-dimensional code space in theinfinite-dimensional Hilbert state space of rotational states of a rigid body. These codes, whichprotect against both drift in the body's orientation and small changes in its angular momentum, maybe well suited for robust storage and coherent processing of quantum information using rotationalstates of a polyatomic molecule. Extensions of such codes to rigid bodies with a symmetry axis arecompatible with rotational states of diatomic molecules, as well as nuclear states of molecules andatoms. We also describe codes associated with general nonabelian compact Lie groups and developorthogonality relations for coset spaces, laying the groundwork for quantum information processingwith exotic configuration spaces.