  We theoretically predict that the Casimir force in vacuum between two Chern
insulator plates can be repulsive (attractive) at long distances whenever the
sign of the Chern numbers characterizing the two plates are opposite (equal). A
unique feature of this system is that the sign of the force can be tuned simply
by turning over one of the plates or alternatively by electrostatic doping. We
calculate and take into account the full optical response of the plates and
argue that such repulsion is a general phenomena for these systems as it relies
on the quantized zero frequency Hall conductivity. We show that achieving
repulsion is possible with thin films of Cr-doped (Bi,Sb)$_2$Te$_3$, that were
recently discovered to be Chern insulators with quantized Hall conductivity.
