  In equilibrium liquid crystals, chirality leads to a variety of spectacular
three-dimensional structures, but chiral and achiral phases with the same
broken continuous symmetries have identical long-time, large-scale dynamics. In
this paper, we demonstrate that chirality qualitatively modifies the dynamics
of layered liquid crystals in active systems in both two and three dimensions
due to an active "odder" elasticity. In three dimensions, we demonstrate that
the hydrodynamics of active cholesterics differs fundamentally from smectic-A
liquid crystals, unlike their equilibrium counterpart. This distinction can be
used to engineer a columnar array of vortices, with anti-ferromagnetic
vorticity alignment, that can be switched on and off by external strain. A
two-dimensional chiral layered state -- an array of lines on an incompressible,
free-standing film of chiral active fluid with a preferred normal direction --
is generically unstable. However, this instability can be tuned in easily
realisable experimental settings, when the film is either on a substrate or in
an ambient fluid.
