  We study perturbative noncommutative quantum gravity by expanding the
gravitational field about a fixed classical background. A calculation of the
one loop gravitational self-energy graph reveals that only the non-planar
graviton loops are damped by oscillating internal momentum dependent factors.
The noncommutative quantum gravity perturbation theory is not renormalizable
beyond one loop for matter-free gravity and all loops for matter interactions.
Comments are made about the nonlocal gravitational interactions produced by the
noncommutative spacetime geometry.
