  We establish the well-posedness of the Neumann problem for stochastic
conservation laws with multiplicative noise. As a major step for establishing
the uniqueness of the kinetic solution to the referred problem we establish the
new strong trace property for stochastic conservation laws. Existence of
kinetic solutions is proved through the vanishing viscosity method and the
detailed analysis of the corresponding stochastic parabolic problem is also
made here for the first time, as far as the authors know.
