  Einstein's Theory of General Relativity was formulated as a gauge theory of
Lorentz symmetry by Utiyama in 1956, while the Einstein-Cartan gravitational
theory was formulated by Kibble in 1961 as the gauge theory of Poincare
transformations. In a noncommutative space-time with canonical commutation
relations between the coordintes, Lorentz symmetry is violated and field
theories constructed on such space-times have instead the so-called twisted
Poincare invariance. In this paper a gauge theory formulation of noncommutative
gravity is proposed based on the twisted Poincare symmetry together with the
requirement of covariance under the general coordinate transformations, an
essential ingredient of the theory of general relativity. The advantages of
such a formulation as well as the related problems are discussed and possible
ways out are outlined.
