We generalize the topological massive gauge model of gravity to a three-dimensional Riemann-Cartan spacetime with torsion. Our Lagrangian consists of the familiar Einstein-Cartan term, the Chern-Simons three-form for the curvature and, in addition, of a new "translational" Chem-Simons term. An exact vacuum solution is derived with purely axial torsion and constant curvature.