The molecular ions HC6- and HC4- have recently been identified both in the laboratory and in astronomical environments. In addition, carbon chain anions have been proposed as potential carriers of the diffuse interstellar bands. Using a selected ion flow tube apparatus, we have determined the rate constants for the reactions of C-n(-) and HCn- with H, N, and O atoms in order to characterize their interstellar chemistry. Reactions between the carbon chain anions and H and O occur readily, with rate constants ranging from mid to high 10(-10) cm(3) s(-1). H atom reactions proceed primarily by associative detachment, and O atom reactions proceed both by associative detachment and by extrusion of CO. Reactions between the carbon chains and N atoms are slower, but the reaction products that are observed could provide a negative ion pathway for the synthesis of observed interstellar species.