  A new heterotic N=2 string with manifest target space supersymmetry is
constructed by combining a conventional N=2 string in the right-moving sector
and a Green-Schwarz-Berkovits type string in the left-moving sector. The
corresponding sigma model is then obtained by turning on background fields for
the massless excitations. We compute the beta functions and we partially check
the OPE's of the superconformal algebra perturbatively in $\alpha'$, all in
superspace. The resulting field equations describe N=1 self-dual supergravity.
