Recent Monte Carlo simulations have demonstrated that a source with a spherical distribution of orbital angular momenta such as the Oort Cloud cannot give rise to the highly flattened distribution of short-period comets. It was also demonstrated that the problem of delivery could be resolved if short-period comets originate in a low inclination disk of comets beyond the orbit of Neptune. Numerical integrations of cometary motion in this disk show that perturbations by the four major planets can result in chaotic motions which, on long timescales, can deliver comets to low inclination Neptune-crossing orbits. Multistage gravitational scattering by the major planets can then, according to theory, supply short-period comets with orbital elements matching observations. 34 refs.