The electronic absorption spectra of mono-hydrogenated carbon chain anions C2nH- (n=5-10) have been measured in the gas-phase and in 6 K neon matrices (n=8-12). The techniques of resonant two-color electron photodetachment in the gas-phase and absorption spectroscopy of mass-selected anions in neon matrix were used. A homologous series is observed, with band system origins shifting from 304 nm for C10H- to 590 nm for C20H-. In conjunction with ab initio calculations the band systems are attributed to a (1)Sigma(+)<-- X (1)Sigma(+) transition of linear acetylenic anions. Another near lying electronic transition due to a second isomer is also apparent for C10H- up to C24H-. Comparison with tables of the known diffuse interstellar bands indicates possible matches for the origin bands of the C18H- and C20H- isomers.