Hori and Vafa recently suggested a mirror symmetry construction for some manifolds with non-negative first Chern class. The mirror partner of such a manifold is a Landau Ginzburg theory (LG for short) or its orbifold with respect to a finite groups action. The proof of validity of this construction was based on calculation of some physical quantities like the ac, cc rings, BPS structure of solitons, D-brane structure, for both of the objects and observing that these coincide. One of the main examples of manifolds fitting the Hori and Vafa construction is hypersurfaces with positive first Chern class. There is a topological quantity which should be related for both objects if they are mirror partners. This is the elliptic genus. Earlier Witten examining the Gepner and Vafa constructions, which preceded the work of Hopi and Vafa, calculated the elliptic genus of the appropriate LG theories. Witten also suggested the exact relation of the elliptic

genus of LG and the topological elliptic genus of the appropriate hypersurface. Namely, for a Calabi-Yau hypersurface the so called two parameter elliptic genus coincides withthe two parameter elliptic genus for the appropriate LG, and for hypersurfaces with spin structure the one parameter elliptic genera coincide. The purpose of this talk is to prove the Witten statement, offering therefore yet another positive test for the Hori-Vafa mirror symmetry construction. We emphasize the role of the chiral de Rham complex in the proof.