  Motivated by a careful analysis of the Laplacian on the supergroup $SU(2|1)$
we formulate a proposal for the state space of the $SU(2|1)$ WZNW model. We
then use properties of $\hat{sl}(2|1)$ characters to compute the partition
function of the theory. In the special case of level $k=1$ the latter is found
to agree with the properly regularized partition function for the continuum
limit of the integrable $sl(2|1) 3-\bar{3}$ super-spin chain. Some general
conclusions applicable to other WZNW models (in particular the case $k=-1/2$)
are also drawn.
