We present the Efficient CH4–CO–OH (ECCOH) chemistry module that allows for the simulation of the methane, carbon monoxide, and hydroxyl radical (CH4–CO–OH) system, within a chemistry climate model, carbon cycle model, or Earth system model. The computational efficiency of the module allows many multi-decadal sensitivity simulations of the CH4–CO–OH system, which primarily determines the global atmospheric oxidizing capacity. This capability is important for capturing the nonlinear feedbacks of the CH4–CO–OH system and understanding the perturbations to methane, CO, and OH, and the concomitant impacts on climate. We implemented the ECCOH chemistry module in the NASA GEOS-5 atmospheric global circulation model (AGCM), performed multiple sensitivity simulations of the CH4–CO–OH system over 2 decades, and evaluated the model output with surface and satellite data sets of methane and CO. The favorable comparison of output from the ECCOH chemistry module (as configured in the GEOS-5 AGCM) with observations demonstrates the fidelity of the module for use in scientific research.