  We study the effects of chiral constituent molecules on the macroscopic
shapes attained by lipid bilayer membranes. Such fluid membranes are beautiful
examples of statistical ensembles of random shapes, sometimes coupled to
in-plane order. We analyze them with methods of continuum elasticity theory,
generalizing the well-known Canham-Helfrich model, and in particular
incorporate the effects of thermal fluctuations. The condition that coordinate
choice be immaterial greatly constrains the possible forms of the statistical
weights in these systems, leading to very few independent couplings and hence
physically simple models. Thermal fluctuations effectively reduce the chirality
of a membrane at long scales, leading to an anomalous scaling relation for the
radius of bilayer tubules and helices as a function of chirality. En route to
this conclusion we develop a perturbative calculation scheme, paying particular
attention to the functional measure needed to describe fluctuations
covariantly. %% [In the new version some TeX problems are fixed. This file was
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