  We show that the stacks of two-dimensional semiconductor crystals with the
chiral packing exhibit optical activity and circular dichroism. We develop a
microscopic theory of these phenomena in the spectral range of exciton
transitions which takes into account the spin-dependent hopping of excitons
between the layers in the stack and the interlayer coupling of excitons via
electromagnetic field. For the stacks of realistic two-dimensional
semiconductors such as transition metal dichalcogenides, we calculate the
rotation and ellipticity angles of radiation transmitted through such
structures. The angles are resonantly enhanced at the frequencies of both
bright and dark exciton modes in the stack. We also study the photoluminescence
of chiral stacks and show that it is circularly polarized.
