  We consider the large N limit of three-dimensional U(N)_k Chern-Simons theory
coupled to a Dirac fermion in the fundamental representation. In this limit, we
compute several correlators to all orders in the `t Hooft coupling N/k. It was
suggested recently that this theory is dual to the Legendre-transformed theory
of scalar fields coupled to Chern-Simons gauge interactions. Our results show
that this duality holds for any value of the `t Hooft coupling, at least at the
level of the planar 3-point functions. In addition, we determine the sign in
the duality transformation of the Chern-Simons level, as well as the relation
between the "triple-trace" deformation which exists in the bosonic Chern-Simons
theory and in the Legendre-transformed fermionic theory.
