  Let M = H^3 / \Gamma be a hyperbolic 3-manifold of finite volume. We show
that if H and K are abelian subgroups of \Gamma and g is in \Gamma, then the
double coset HgK is separable in \Gamma. As a consequence we prove that if M is
a closed, orientable, Haken 3-manifold and the fundamental group of every
hyperbolic piece of the torus decomposition of M is conjugacy separable then so
is the fundamental group of M. Invoking recent work of Agol and Wise, it
follows that if M is a compact, orientable 3-manifold then \pi_1(M) is
conjugacy separable.
