The reaction of small ligands within the distal pocket of haem proteins such as myoglobin, to form ligated, low-spin iron complexes is an archetypal spin-forbidden process in bioinorganic chemistry, because the initial, "deoxy" iron complex has a high-spin ground state. Density functional theory (DFT), transition-state theory (TST), and hybrid DFT/molecular mechanics (QM/MM) calculations are reported on the carbon monoxide reaction. Using DFT data for a model compound, TST rate calculations at room temperature are carried out which give fair agreement with experiment, and suggest a highly non-adiabatic nature to the reaction. QM/MM calculations on the whole protein are reported, which are in qualitative agreement with the gas-phase model results, but suggest that protein matrix effects on the reaction rate may be important.