We present full in situ structural solutions of carbon dioxide hydrate-II and hydrogen hydrate C0 at elevated pressures using neutron and X-ray diffraction. We find both hydrates adopt a common water network structure. The structure exhibits several features not previously found in hydrates; most notably it is chiral and has large open spiral channels along which the guest molecules are free to move. It has a network that is unrelated to any experimentally known ice, silica, or zeolite network but is instead related to two Zintl compounds. Both hydrates are found to be stable in electronic structure calculations, with hydration ratios in very good agreement with experiment.