In this talk we provide both a diagnosis and resolution of the cosmological constant problem, one in which a large (as opposed to a small) cosmological constant $\Lambda$ can be made compatible with observation. We trace the origin of the cosmological constant problem to the assumption that Newton's constant $G$ sets the scale for cosmology. And then we show that once this assumption is relaxed (so that the local $G$ as measured in a local Cavendish experiment is no longer to be associated with global cosmology), the very same cosmic acceleration which has served to make the cosmological constant problem so very severe instead then serves to provide us with its potential resolution. In particular we show that no matter how large $\Lambda$ itself might be, in an accelerating universe the actual measureable contribution of $\Lambda$ to cosmology, viz. $\Omega_{\Lambda}$, can still be small today simply because the universe is as old as it is. (Reference: astro-ph/9910093).