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A family of semiconductors called as Chern band insulator are shown to hostexciton bands with non-zero topological Chern integers and chiral exciton edgemodes. Using a prototypical two-band Chern insulator model, we calculate across-correlation function to obtain the exciton bands and their Chernintegers. The lowest exciton band acquires Chern integers such as $\pm 1$ and$\pm 2$ in electronic Chern insulator phase. The non-trivial topology can beexperimentally observed both by non-local optoelectronic response of excitonedge modes and by a phase shift in the cross-correlation response due to thebulk mode. Our result suggests that magnetically doped HgTe, InAs/GaSb quantumwells and $\text{(Bi,Sb)}_{2} \text{Te}_{3}$ thin film are promising candidatesfor a platform of topological excitonics.

Chiral Topological Excitons in a Chern Band Insulator