Various methods have been proposed for mitigating release of anthropogenic CO2 to the atmosphere, including deep-sea injection of CO2 captured from fossil-fuel fired power plants. Here, we use a schematic model of ocean chemistry and transport to analyze the geochemical consequences of a new method for separating carbon dioxide from a waste gas stream and sequestering it in the ocean. This method involves reacting CO2-rich power-plant gases with seawater to produce a carbonic acid solution which in turn is reacted on site with carbonate mineral (e.g., limestone) to form Ca2+ and bicarbonate in solution, which can then be released and diluted in the ocean. Such a process is similar to carbonate weathering and dissolution which would have otherwise occurred naturally, but over many millennia. Relative to atmospheric release or direct ocean CO2 injection, this method would greatly expand the capacity of the ocean to store anthropogenic carbon while minimizing environmental impacts of this carbon on ocean biota. This carbonate-dissolution technique may be more cost-effective and less environmentally harmful, and than previously proposed CO2 capture and sequestration techniques.