We consider the quantum gravity and cosmology of a Jordan-Brans-Dicke theory. Its constraint algebra is that of general relativity, as a consequence of the general covariance of scalar-tensor theories. We propose that boundary conditions must be imposed in the Jordan frame, in which particles satisfy the strong equivalence principle. We discuss both Hartle-Hawking and wormhole boundary conditions in the context of quantum cosmology. Wormholes may affect the constants of nature and, in particular, the Brans-Dicke parameter. Following Coleman's mechanism, we find a probability distribution for wormhole configurations which is strongly peaked at zero cosmological constant and infinite Brans-Dicke parameter. That is, we recover general relativity as the effective low energy theory of gravity.