We propose a new implicit computational fluid dynamics method for steady-state compressible reacting flows. The concept is to decouple the total mass, momentum, and energy conservation equations from the species mass and internal energy equations, and to solve the two equation sets sequentially. With certain approximations to the implicit system, it is possible to dramatically reduce the cost of the solution with little to no penalty on convergence properties for many problems. The cost of the decoupled implicit problem scales linearly with the number of species, as opposed to the quadratic scaling for the conventional fully-coupled method. Furthermore, the method reduces the memory requirements by a significant factor. We find that the performance of the method decreases as the relative reaction rates become very large and when the reactions are strongly exothermic. Several approaches are explored to improve the performance of the method for these cases. The decoupled implicit method shows promise for application to aerothermodynamics problems and reacting flows.