Significant gas-phase chemistry occurs in the comae of bright comets, as is demonstrated here for the case of Comet Hale-Bopp. The abundance ratio of the two isomers, hydrogen cyanide and hydrogen isocyanide, is shown to vary with heliocentric distance in a way that is consistent with production of HNC by ion-molecule chemistry initiated by the photoionization of water. Likewise, the first maps of emission from HCO+ show an abundance and an extended distribution that are consistent with the same chemical model.