High-resolution proton and natural abundance carbon-13 NMR spectra of a rigid chiral molecule, (+/-)-beta-(trichloromethyl)-beta-propiolactone, dissolved in the liquid-crystalline phase of poly(gamma-benzyl-L-glutamate) (PBLG), in methylene chloride, were analyzed. From the NMR data and the X-ray structure, the full order matrix was determined and analyzed in detail for each optical isomer of the molecule. It is shown that the spectral discrimination of the enantiomers in this lyotropic medium arises mainly from the difference in their average molecular orientation and the principal axis systems of orientation are compared.