The excess volumes of fluid mixtures are evidently related to fluid structure. Especially at high densities, they should be very sensitive to packing effects, and thus, to the shape of molecules. In order to separate the shape effects from effects of attractive interactions, model fluids consisting of fused-hard-sphere molecules with realistic dimensions have been studied. This work especially deals with mixtures of enantiomers. Extensive Monte Carlo simulations, using the NpT ensemble technique as well as a newly developed multiensemble technique for the direct determination of excess volumes, have been performed for two chiral molecules, CHFCII and 4-vinylcyclohexene. In both cases, weakly positive excess volumes occur at high pressures. Thermodynamic arguments point to an instability of the investigated racemic mixtures at high pressures, which might induce demixing or a conversion reaction and finally lead to a spontaneous imbalance of enantiomers in macroscopic phases. The importance of this observation for the origin of biological enantioselectivity on Earth is discussed.