  Chiral fluctuations in triangular antiferromagnets (TAFs) at $T \ll T_N$ are
studied theoretically. The case of a ferromagnetic interaction along c axis
(which is directed perpendicular to the plane of the lattice),
Dzyaloshinskii-Moriya interaction ${\bf D}\| c$ and a weak magnetic field ${\bf
H}\| c$ is considered in detail. Previously, this model has been proposed to
describe quantum TAF CsCuCl$_3$. Expressions for dynamical chirality (DC) are
derived within the linear spin-wave approximation. In contrast to
non-frustrated antiferromagnets, DC is found to be nonzero even at $D,H=0$ in a
one-domain sample. We argue that this unusual behavior stems from the fact that
a ground state of XY and Heisenberg TAFs is characterized by an axial vector
along which DC is directed.
