N=2 supergravity in three dimensions and its Godel supersymmetric background

The four dimensional Godel spacetime is known to have the structure M_3 x R. It is also known that the three-dimensional factor M_3 is an exact solution of three-dimensional gravity coupled to a Maxwell-Chern-Simons theory. We build in this paper a N=2 supergravity extension for this action and prove that the Godel background preserves half of all supersymmetries.