  We describe the construction of $2+1$-dimensional toplogically massive adS
gravity with ${\mathcal{N}}$-extended supersymmetry in superspace by means of
introducing a compensating hypermultiplet for the super-Weyl invariance. For
$\mathcal{N}\geq 3$ 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
$\mathcal{N}\geq 4$. For $\mathcal{N}= 4$ we show that this leads to
topologically massive gravity at the chiral point and construct the
corresponding off-shell component action.
