We present the theory describing supersymmetrical vortices in the curved superspace of the (1,0) supergravity. The action is defined as a (1,0) locally supersymmetric $SU(2)/U(1)$ coset perturbed by the cosmological constant-like term. The perturbation is such that it preserves the integrability of the coset model. Because of supersymmetry the perturbed theory is an exact quantum system provided a proper dilaton is taken into account. The exact value of the dilaton is determined in the supersymmetric case by the quasi-classical background of the bosonic coset.

UMDPP 94-074, QMW 93-35, 14 pages