A survey of 15 lines of sight for the CN B /sup 2/..sigma../sup +/--X /sup 2/..sigma../sup +/ interstellar absorption lines shows that the CN column density in diffuse interstellar clouds follows the relation log N(CN)proportionalm log N(H/sub 2/), where mroughly-equal3. This result is reproduced by a reaction network in which CN is produced primarily from C/sub 2/ by the neutral-neutral reaction C/sub 2/+N ..-->.. CN+C, and photodissociation is the main destruction pathway for the neutral molecules CH, C/sub 2/, and CN. The CN radical is the first molecular species observed in diffuse clouds that requires a neutral-neutral reaction for its formation in the gas phase. The network also reproduces the observed ratio N(CN)/N(H/sub 2/).