  We define a theory of gravity by constructing a gravitational holonomy
operator in twistor space. The theory is a gauge theory whose Chan-Paton factor
is given by a trace over elements of Poincar\'{e} algebra and Iwahori-Hecke
algebra. This corresponds to a fact that, in a spinor-momenta formalism,
gravitational theories are invariant under spacetime translations and
diffeomorphism. The former symmetry is embedded in tangent spaces of frame
fields while the latter is realized by a braid trace. We make a detailed
analysis on the gravitational Chan-Paton factor and show that an S-matrix
functional for graviton amplitudes can be expressed in terms of a
supersymmetric version of the holonomy operator. This formulation will shed a
new light on studies of quantum gravity and cosmology in four dimensions.
