  We construct a string theory in three-dimensional anti-de Sitter space-time
that is independent of the boundary metric. It is a topologically twisted
theory of quantum gravity. We study string theories with an asymptotic N=2
superconformal symmetry and demonstrate that, when the world sheet coupling to
the space-time boundary metric undergoes a U(1) R-symmetry twist, the
space-time boundary energy-momentum tensor becomes topological. As a by-product
of our analysis, we obtain the world sheet vertex operator that codes the
space-time energy-momentum for conformally flat boundary metrics.
