Stabilizing the concentration of atmospheric CO
2
may require storing enormous quantities of captured anthropogenic CO
2
in near-permanent geologic reservoirs. Because of the subsurface temperature profile of terrestrial storage sites, CO
2
stored in these reservoirs is buoyant. As a result, a portion of the injected CO
2
can escape if the reservoir is not appropriately sealed. We show that injecting CO
2
into deep-sea sediments <3,000-m water depth and a few hundred meters of sediment provides permanent geologic storage even with large geomechanical perturbations. At the high pressures and low temperatures common in deep-sea sediments, CO
2
resides in its liquid phase and can be denser than the overlying pore fluid, causing the injected CO
2
to be gravitationally stable. Additionally, CO
2
hydrate formation will impede the flow of CO
2
(l) and serve as a second cap on the system. The evolution of the CO
2
plume is described qualitatively from the injection to the formation of CO
2
hydrates and finally to the dilution of the CO
2
(aq) solution by diffusion. If calcareous sediments are chosen, then the dissolution of carbonate host rock by the CO
2
(aq) solution will slightly increase porosity, which may cause large increases in permeability. Karst formation, however, is unlikely because total dissolution is limited to only a few percent of the rock volume. The total CO
2
storage capacity within the 200-mile economic zone of the U.S. coastline is enormous, capable of storing thousands of years of current U.S. CO
2
emissions.