  Three dimensional Euclidean pure gravity with a negative cosmological
constant can be formulated in terms of the Chern-Simons theory, classically.
This theory can be written in a supersymmetric way by introducing auxiliary
gauginos and scalars. We calculate the exact partition function of this
Chern-Simons theory by using the localization technique. Thus, we obtain the
quantum gravity partition function, assuming that it can be obtained
non-perturbatively by summing over partition functions of the Chern-Simons
theory on topologically different manifolds. The resultant partition function
is modular invariant, and in the case in which the central charge is expected
to be 24, it is the J-function, predicted by Witten.
