  Similar to QCD, general relativity has a $\Theta$ sector due to large
diffeomorphisms. We make explicit, for the first time, that the gravitational
CP violating $\Theta$ parameter is non-perturbatively related to the
cosmological constant. A gravitational pseudoscalar coupling to massive
fermions gives rise to general relativity from a topological $B\wedge F$ theory
through a chiral symmetry breaking mechanism. We show that a gravitational
Peccei-Quinn like mechanism can dynamically relax the cosmological constant.
