  Statistical ensembles of flexible two-dimensional fluid membranes arise
naturally in the description of many physical systems. Typically one encounters
such systems in a regime of low tension but high stiffness against bending,
which is just the opposite of the regime described by the Polyakov string. We
study a class of couplings between membrane shape and in-plane order which
break 3-space parity invariance. Remarkably there is only {\it one} such
allowed coupling (up to boundary terms); this term will be present for any
lipid bilayer composed of tilted chiral molecules. We calculate the
renormalization-group behavior of this relevant coupling in a simplified model
and show how thermal fluctuations effectively reduce it in the infrared.
