The transport of small ligands to active sites of proteins is the basis of vital processes in biology such as enzymatic catalysis and cell signaling, but also of more destructive ones including enzyme inhibition and oxidative damage. Here, we show how a diffusion-reaction model solved by means of molecular dynamics and density functional theory calculations provides novel insight into the transport of small ligands in proteins. In particular, we unravel the existence of an elusive, dynamically formed gas channel, which CO2 takes to diffuse from the solvent to the active site (C-cluster) of the bifunctional multisubunit enzyme complex carbon monoxide dehydrogenase/acetyl-CoA synthase (CODH/ACS). Two cavities forming this channel are temporarily created by protein fluctuations and are not apparent in the X-ray structures. The ligand transport is controlled by two residues at the end of this tunnel, His113 and His 116, and occurs on the same time scale on which chemical binding to the active site takes place (0.1-1 ms), resulting in an overall binding rate on the second time scale. We find that upon reduction of CO2 to CO, the newly formed Fe-hydroxy ligand greatly strengthens the hydrogen-bond network, preventing CO from exiting the protein through the same way that CO2 takes to enter the protein. This is the basis for directional transport of CO from the production site (C-cluster of CODH subunit) to the utilization site (A-cluster of ACS subunit). In view of these results, a general picture emerges of how large proteins guide small ligands toward their active sites.