  We discuss optical chirality in different types of gyrotropic media. Our
analysis is based on the formalism of nongeometric symmetries of Maxwell's
equations in vacuum generalized to material media with given constituent
relations. This approach enables us to derive directly conservation laws
related to the nongeometric symmetries. For isotropic chiral media, we
demonstrate that likewise free electromagnetic field, both duality and helicity
generators belong to the basis set of nongeometric symmetries that guarantees
the conservation of optical chirality. In gyrotropic crystals, which exhibit
natural optical activity, the situation is quite different from the case of
isotropic media. For light propagating along certain crystallographic
direction, there arise two distinct cases, i.~e., (1) the duality is broken but
the helicity is preserved, or (2) only the duality symmetry survives. We show
that the existence of one of these symmetries (duality or helicity) is enough
to define optical chirality. In addition, we present examples of low-symmetry
media, where optical chirality can not be defined.
