  Chiral active materials display odd dynamical effects in both their elastic
and viscous responses. We show that the most symmetric mesophase with
two-dimensional odd elasticity in three dimensions is chiral, polar and
columnar, with two-dimensional translational order in the plane perpendicular
to the columns and no elastic restoring force for their relative sliding. We
derive its hydrodynamic equations from those of a chiral active variant of
model H. The most striking prediction of the odd dynamics is two distinct types
of column oscillation whose frequencies do not vanish at zero wavenumber. In
addition, activity leads to a buckling instability coming from the generic
force-dipole active stress analogous to the mechanical Helfrich-Hurault
instability in passive materials, while the chiral torque-dipole active stress
fundamentally modifies the instability by the selection of helical column
undulations.
