A spatial structure for which mirror reflection cannot be represented by rotations and translations is chiral. For photonic crystals and metamaterials, chirality implies the possibility of circular dichroism, that is, that the propagation of left-circularly polarized light may differ from that of right-circularly polarized light. Here we draw attention to chiral sheet-or surface-like geometries based on chiral triply-periodic minimal surfaces. Specifically we analyse two photonic crystal designs based on the C(Y) minimal surface, by band structure analysis and by scattering matrix calculations of the reflection coefficient, for high-dielectric contrasts.