  A rotating star's oblateness creates a deformation in the gravitational field
outside the star, which is measured by the quadrupole-moment tensor. We
consider the effect of the quadrupole moment on the orbital motion and rate of
inspiral of a compact binary system, composed of neutron stars and/or black
holes. We find that in the case of circular orbits, the quadrupole-monopole
interaction affects the relation between orbital radius and angular velocity,
and also the rate of inspiral, by a quantity of order (v/c)^4, where v is the
orbital velocity and c the speed of light.
