  We present the next-to-next-to-leading order post-Newtonian (PN) spin-orbit
Hamiltonian for two self-gravitating spinning compact objects. If at least one
of the objects is rapidly rotating, then the corresponding interaction is
comparable in strength to a 3.5PN effect. The result in the present paper in
fact completes the knowledge of the post-Newtonian Hamiltonian for binary
spinning black holes up to and including 3.5PN. The Hamiltonian is checked via
known results for the test-spin case and via the global Poincare algebra with
the center-of-mass vector uniquely determined by an ansatz.
