  The gauging of the q-Poincar\'e algebra of ref. hep-th 9312179 yields a
non-commutative generalization of the Einstein-Cartan lagrangian. We prove its
invariance under local q-Lorentz rotations and, up to a total derivative, under
q-diffeomorphisms. The variations of the fields are given by their q-Lie
derivative, in analogy with the q=1 case. The algebra of q-Lie derivatives is
shown to close with field dependent structure functions. The equations of
motion are found, generalizing the Einstein equations and the zero-torsion
condition.
