Recent interest in the reflected quasipotential comes from the queueing theory literature, specifically the analysis of so-called reflected Brownian motion where it is the large deviation rate function for the stationary distribution. Our purpose here is to characterize the reflected quasipotential in terms of a first-order Hamilton-Jacobi equation. Using conventional dynamic programming ideas, along with a complementarity problem formulation of the effect of the Skorokhod map on absolutely continuous paths, we will derive necessary conditions in the form of viscosity-sense boundary conditions. It turns out that even with these boundary conditions solutions are not unique. Thus a unique characterization needs to refer to some additional property of . We establish such a characterization in two dimensions.