  We present a teleparallel complex gravity as the foundation for the
formulation of noncommutative gravity theory. The negative energy ghosts in the
conventional formulation with U(1,3) local Lorentz connection no longer exists,
since the local Lorentz invariance is broken down to U(1,3) global Lorentz
symmetry. As desired, our teleparallel complex gravity theory also passes the
key classical test of perihelion advance of Mercury. Based on this result, we
present a lagrangian for the noncommutative teleparallel gravity theory.
