Topologically massive gravity with extended supersymmetry

We describe the construction of 2 + 1-dimensional toplogically massive anti-de Sitter gravity with N-extended supersymmetry in superspace by means of introducing a compensating hypermultiplet for the super-Weyl invariance. For N >= 3, the scalar multiplet must be on shell and the potential for the scalar compensator is completely determined by the geometry. As a consequence, the resulting massive theory has no free parameter for N >= 4. For N = 4, we show that this leads to topologically massive gravity at the chiral point and construct the corresponding off-shell component action.