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The't Hooft expansion of SU (N) Chern-Simons theory on S'3 is proposed to be exactly dual to the topological closed string theory on the S2 blow up of the conifold geometry. The B-field on the S2 has magnitude iV^= A, the't Hooft coupling. We are able to make a number of checks, such as finding exact agreement at the level of the partition function computed on both sides for arbitrary A and to all orders in 1/7V. Moreover, e-print archive: http://xxx. lanLgov/hep-th/9811131