  We present a scheme to realize the chiral topological excitonic insulator in
semiconductor heterostructures which can be experimentally fabricated with a
coupled quantum well adjacent to twoferromagnetic insulating films. The
different mean-field chiral topological orders, which are due to the change in
the directions of the magnetization of the ferromagnetic films, can be
characterized by the TKNN numbers in the bulk system as well as by the winding
numbers of the gapless states in the edged system. Furthermore, we propose an
experimental scheme to detect the emergence of the chiral gapless edge state
and distinguish different chiral topological orders by measuring the thermal
conductance.
