The potential energy surfaces associated with the reactions of chromium oxide cation (CrO+) with ethylene have been characterized using density functional, coupled-cluster, and multireference methods. Our calculations show that the most probable reaction involves the formation of acetaldehyde and Cr+ via a hydride transfer involving the metal center. Our calculations support previous experimental hypotheses that a four-membered ring intermediate plays an important role in the reactivity of the system. We have also characterized a number of viable reaction pathways that lead to other products, including ethylene oxide. Due to the experimental observation that CrO+ can activate carbon - carbon bonds, a reaction pathway involving C - ond cleavage has also been characterized. Since many of the reactions involve a change in the spin state in going from reactants to products, locations of these spin surface crossings are presented and discussed. The applicability of methods based on Hartree - k orbitals is also discussed.