Understanding greenhouse gas–climate processes and feedbacks is a fundamental step in understanding climate variability and its links to greenhouse gas fluxes. Chemical transport models are the primary tool for linking greenhouse gas fluxes to their atmospheric abundances. Hence, accurate simulations of greenhouse gases are essential. Here, we present a new simulation in the GEOS-Chem chemical transport model that couples the two main greenhouse gases—carbon dioxide (CO2) and methane (CH4)—along with the indirect greenhouse gas carbon monoxide (CO) based on their chemistry. Our updates include the online calculation of the chemical production of CO from CH4 and the online production of CO2 from CO, both of which were handled offline in the previous versions of these simulations. In the newly developed coupled (online) simulation, we used consistent hydroxyl radical (OH) fields for all aspects of the simulation, resolving biases introduced by inconsistent OH fields in the currently available uncoupled (offline) CH4, CO and CO2 simulations. We compare our coupled simulation with the existing v12.1.1 GEOS-Chem uncoupled simulations run the way they are currently being used by the community. We discuss differences between the uncoupled and coupled calculation of the chemical terms and compare our results with surface measurements from the NOAA Global Greenhouse Gas Reference Network (NOAA GGGRN), total column measurements from the Total Carbon Column Observing Network (TCCON) and aircraft measurements from the Atmospheric Tomography Mission (ATom). Relative to the standard uncoupled simulations, our coupled results suggest a stronger CO chemical production from CH4, weaker production of CO2 from CO and biases in the OH fields. However, we found a significantly stronger chemical production of CO2 in tropical land regions, especially in the Amazon. The model–measurement differences point to underestimated biomass burning emissions and secondary production for CO. The new self-consistent coupled simulation opens new possibilities when identifying biases in CH4, CO and CO2 source and sink fields, as well as a better understanding of their interannual variability and co-variation.