This paper considers the problem of H∞ output feedback controller design for stochastic nonlinear systems. The synthesis of the controller is based on the concept of dissipativity for stochastic systems which was introduced by the authors in a previous work. The stochastic dissipativity concept facilitates the establishment of a bounded real lemma (BRL) for stochastic systems, on the basis of which the the theory of this paper is developed. To facilitate the output controller design we prescribe an observer structure which results, together with the underlying system, in a Hamilton-Jacobi inequality of 2n variables. With the aid of this Hamilton-Jacobi inequality we establish sufficient conditions for the solution of the H∞ output feedback problem for nonlinear stochastic systems in terms of two coupled Hamilton-Jacobi inequalities.