  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 charge-dipole
interaction ($a/R^2$). We show that prominent candidate molecules such as KRb
and deuterated hydroxyl (OD) should bind to Rydberg rubidium atoms, with
energies $E_b\simeq 5-25$ GHz at distances $R\simeq 0.1-1 \ \mu$m. These
molecules form in double wells, mimicking chiral molecules, with each well
containing a particular dipole orientation. We prepare a set of correlated
dressed electron-dipole eigenstates which are used in a resonant Raman scheme
to coherently control the dipole orientation and to create cat-like entangled
states of the polar molecule.
