  We define the general Hill system and briefly analyze its dynamical behavior.
A particular Hill system representing the interaction of a Keplerian binary
system with a normally incident circularly polarized gravitational wave is
discussed in detail. In this case, we compute the Poincar\'e-Melnikov function
explicitly and determine its zeros. Moreover, we provide numerical evidence in
favor of chaos in this system. The partially averaged equations for the Hill
system are used to predict the regular behavior of the Keplerian orbit at
resonance with the external radiation.
