This paper outlines a new CaCO3 calcination method for producing a stream of CO2 (suitable for permanent geological storage after purification and compression). The process is based on the use of very hot CaO particles (T >1000 degrees C) to transfer heat from a circulating fluidized bed combustor (CFBC) to a calciner (fluidized with CO2 and/or steam). Since the fluidized bed combustor and calciner have separate atmospheres, the CO2 resulting from the decomposition of CaCO3 can be captured, while the CO2 generated in the combustion of the fuel in air is emitted to the atmosphere. We demonstrate that with this system it is possible to reduce the CO2 emissions of a cement plant by around 60%. Furthermore, since the key pieces of equipment are similar to the commercial CFBCs used in power generation plants, it is possible to establish the additional investment required for the system and to estimate the cost per ton of CO2 avoided for this process to be about 19 $/tCO2 avoided.