We study a sp(3) bonded chiral framework structure (CFS) composed of the group 14 elements carbon (C), silicon (Si), germanium (Ge), or tin (Sn). The CFS is very simple and highly symmetric, having a six-atom primitive unit cell with all atoms being equivalent. The CFS is the elemental analog of a zeolite-type structure and is also related to clathrate structures. Density-functional theory calculations show that the CFS is only slightly higher in energy than the diamond structure, with an energy difference varying from 112 meV per atom for C to 28 meV per atom for Sn. The bulk modulus of the carbon CFS is found to be smaller than that of diamond but larger than that of the carbon clathrate II structure. The density of electronic states and band gaps of the elemental CFS materials are described and compared with those of the corresponding diamond structures.