We describe a parallel and quasi-explicit Discontinuous Galerkin (DG) kinetic scheme for solving hyperbolic systems of conservation laws. The solver is unconditionally stable (i.e., the CFL number can be arbitrary), has the complexity of an explicit scheme. The time integration can be fully time reversible. It can be applied to any hyperbolic system of balance laws. In this work, we assess the performance of the scheme in the particular cases of the Maxwell’s equations. We measure the benefit of the unconditional stability by performing experiments with very large CFL numbers. In addition, the parallel possibilities of the method are investigated.