  We show how to write an off-shell action for the $SU(2)\times U(1)$
supersymmetric WZW model in terms of $N=2$ chiral and twisted chiral
multiplets. We discuss the $N=4$ supersymmetry of this model and exhibit the
$N=4$ superconformal current algebra. Finally, we show that the off-shell
formulation makes it possible to perform a duality transformation, which leads
to a supersymmetric sigma model on a manifold with a black hole type
singularity.
