  We calculate the relativistic constraint equation which relates the curvature
perturbation to the matter density contrast at second order in cosmological
perturbation theory. This relativistic "second order Poisson equation" is
presented in a gauge where the hydrodynamical inhomogeneities coincide with
their Newtonian counterparts exactly for a perfect fluid with constant equation
of state. We use this constraint to introduce primordial non-Gaussianity in the
density contrast in the framework of General Relativity. We then derive
expressions that can be used as initial conditions of N-body codes for
structure formation which probe the observable signature of primordial
non-Gaussianity in the statistics of the evolved matter density field.
