In this paper,we extended the random Melnikov method for the stochastic driven systems with continuous vector field to the discontinuous systems driven by a random disordered periodic under the assumption that the unperturbed system is a piecewise Hamiltonian system By measuring the distance of the perturbed stable and unstable manifolds,the nonsmooth random Melnikov process can be derived in detail,and then the mean-square criterion of the onset of chaos is established in statisticals sense.