Density functional theory and transition state theory rate constant calculations have been performed to gain insight into the bimolecular reaction of the Criegee intermediate (CI) with carbon monoxide (CO) that is proposed to be important in both atmospheric and industrial chemistry. A new mechanism is suggested in which the CI acts as an oxidant by transferring an oxygen atom to the CO, resulting in the formation of a carbonyl compound (aldehyde or ketone depending upon the CI) and carbon dioxide. Fourteen different CIs, including ones resulting from biogenic ozonolysis, are considered. Consistent with previous reports for other CI bimolecular reactions, the anti conformers are found to react faster than the syn conformers. However, this can be attributed to steric effects and not hyperconjugation as generally invoked. The oxidation reaction is slow, with barrier heights between 6.3 and 14.7 kcal/mol and estimated reaction rate constants 6-12 orders-of-magnitude smaller than previously reported literature estimates. The reaction is thus expected to be unimportant in the context of tropospheric oxidation chemistry. However, the reaction mechanism suggests that CO could be exploited in ozonolysis to selectively obtain industrially important carbonyl compounds.