  A gauge theory of gravity is defined in 6 dimensional non-commutative
space-time. The gauge group is the unitary group U(2,2), which contains the
homogeneous Lorentz group, SO(4,2), in 6 dimensions as a subgroup. It is shown
that, after the Seiberg-Witten map, in the corresponding theory the lowest
order corrections are first order in the non-commutativity parameter \theta.
This is in contrast with the results found in non-commutative gauge theories of
gravity with the gauge group SO(d,1).
