  Generalizing work of Gross--Zagier and Schofer on singular moduli, we study
the CM values of regularized theta lifts of harmonic Whittaker forms. We
compute the archimedian part of the height pairing of arithmetic special
divisors and CM cycles on Shimura varieties associated to certain quadratic
spaces over an arbitrary totally real base field. As a special case, we obtain
an explicit formula for the norms of the CM values of those meromorphic modular
forms arising as regularized theta lifts of holomorphic Whittaker forms.
