  We prove that any word hyperbolic group which is virtually compact special
(in the sense of Haglund and Wise) is conjugacy separable. As a consequence we
deduce that all word hyperbolic Coxeter groups and many classical small
cancellation groups are conjugacy separable.
  To get the main result we establish a new criterion for showing that elements
of prime order are conjugacy distinguished. This criterion is of independent
interest; its proof is based on a combination of discrete and profinite
(co)homology theories.
