  Binary systems of rapidly spinning compact objects, such as black holes or
neutron stars, are prime targets for gravitational wave astronomers. The
dynamics of these systems can be very complicated due to spin-orbit and
spin-spin couplings. Contradictory results have been presented as to the nature
of the dynamics. Here we confirm that the dynamics - as described by the second
post-Newtonian approximation to general relativity - is chaotic, despite claims
to the contrary. When dissipation due to higher order radiation reaction terms
are included, the chaos is dampened. However, the inspiral-to-plunge transition
that occurs toward the end of the orbital evolution does retain an imprint of
the chaotic behaviour.
