  Chiral molecules form a number of non-chiral structures, the simplest being
an isotropic fluid phase. In a mesophase of achiral molecules the fluctuations
will on average be achiral as well: left-handed twists and right-handed twists
will occur with the same probability. In a system composed of chiral molecules,
however, the fluctuations will be biased in one direction or the other, and
there will be optical effects such as a non-zero fluctuation induced rotary
power {\sl in addition} to the molecular rotary power of the individual
molecules. We discuss this effect in a number of contexts, including lyotropic
lamellar phases. When the tendency to twist is strong enough or the line energy
of having an exposed edge is small enough, a new, defect riddled ground state
of a lyotropic lamella, akin to the Renn-Lubensky twist-grain-boundary phase of
thermotropic smectics, can occur.
