In an Endex reactor endothermic and exothermic reactions are directly thermally coupled and kinetically matched to achieve intrinsic thermal stability, efficient conversion, autothermal operation, and minimal heat losses. Applied to the problem of in-line carbon dioxide separation from flue gas, Endex principles hold out the promise of effecting a carbon dioxide capture technology of unprecedented economic viability. In this work we describe an Endex Calcium Looping reactor, in which heat released by chemisorption of carbon dioxide onto calcium oxide is used directly to drive the reverse reaction, yielding a pure stream of carbon dioxide for compression and geosequestration. In this initial study we model the proposed reactor as a continuous-flow dynamical system in the well-stirred limit, compute the steady states and analyse their stability properties over the operating parameter space, flag potential design and operational challenges, and suggest an optimum regime for effective operation.