  We consider three dimensional gravity with a positive cosmological constant
and non- zero gravitational Chern-Simons term. This theory has inflating de
Sitter solutions and local metric degrees of freedom. The Euclidean signature
partition function of the theory is evaluated including both perturbative and
non-perturbative corrections. The perturbative one-loop correction is computed
using heat kernel techniques. The non- perturbative corrections come from
gravitational instantons with non-trivial topology which can be enumerated
explicitly. We compute the sum over an infinite class of ge- ometries and show
that, unlike the case of pure Einstein gravity, the partition function is
finite. This demonstrates that the inclusion of non-trivial local degrees of
freedom can render the sum over geometries convergent.
