The abundance ratio of the isomers HCN and HNC has been investigated in comet Hale-Bopp (C/1995 O1) through observations of the J = 4-3 rotational transitions of both species for heliocentric distances 0.93 < r < 3 AU, both pre- and post-perihelion. After correcting for the optical depth of the stronger HCN line, we find that the column density ratio of HNC/HCN in our telescope beam increases significantly as the comet approaches the Sun. We compare this behavior to that predicted from an ion-molecule chemical model and conclude that the HNC is produced in significant measure by chemical processes in the coma; i.e., for comet Hale-Bopp, HNC is not a parent molecule sublimating from the nucleus.