We studied monatomic linear carbon chains stabilized by gold nanoparticles attached to their ends and deposited on a solid substrate. We observe spectral features of straight chains containing from 8 to 24 atoms. Low-temperature PL spectra reveal characteristic triplet fine structures that repeat themselves for carbon chains of different lengths. The triplet is invariably composed of a sharp intense peak accompanied by two broader satellites situated 15 and 40 meV below the main peak. We interpret these resonances as an edge-state neutral exciton and positively and negatively charged trions, respectively. The time-resolved PL shows that the radiative lifetime of the observed quasiparticles is about 1 ns, and it increases with the increase of the length of the chain. At high temperatures a nonradiative exciton decay channel appears due to the thermal hopping of carriers between parallel carbon chains. Excitons in carbon chains possess large oscillator strengths and extremely low inhomogeneous broadenings.