We predict the existence of a class of ultracold giant molecules formed from trapped ultracold Rydberg atoms and polar molecules. The interaction which leads to the formation of such molecules is the anisotropic, long-range charge-dipole interaction. We show that prominent candidate molecules such as deuterated hydroxyl (OD) and KRb should bind to Rydberg rubidium atoms, with energies Eb?5–25GHz at distances R?0.1–1?m. These molecules form in double wells, mimicking chiral molecules, with each well containing a particular dipole orientation. We prepare a set
