The composition of ices in comets may reflect that of the molecular cloud in which the Sun formed, or it may show evidence of chemical processing in the pre-planetary accretion disk around the proto-Sun. As carbon monoxide (CO) is ubiquitous in molecular clouds, its abundance with respect to water could help to determine the degree to which pre-cometary material was processed, although variations in CO abundance may also be influenced by the distance from the Sun at which comets formed. Observations have not hitherto provided an unambiguous measure of CO in the cometary ice (native CO). Evidence for an extended source of CO associated with comet Halley was provided by the Giotto spacecraft, but alternative interpretations exist. Here we report observations of comet Hale-Bopp which show that about half of the CO in the comet comes directly from ice stored in the nucleus. The abundance of this CO with respect to water (12 per cent) is smaller than in quiescent regions of molecular clouds, but is consistent with that measured in proto-stellar envelopes, suggesting that the ices underwent some processing before their inclusion into Hale-Bopp. The remaining CO arises in the coma, probably through thermal destruction of more complex molecules.