Optical bands from the (3)Sigma(u)(-) <-- X (3)Sigma(g)(-) transition of the linear carbon chains HC7H, HC9H, HC11H, and HC13H have been measured in the gas phase by cavity ringdown spectroscopy. The bands exhibit well resolved P and R branches, which for HC7H are partially rotationally resolved. Comparisons between observed and simulated spectra indicate broadening in excess of that expected from the laser linewidth and Doppler width, suggesting rapid radiationless transitions in roughly 0.1-0.01 ns, a time scale consistent with the absence of observed fluorescence from these molecules. The HC7H and HC9H bands are of nearly equal strength, but those of the shorter chain HC5H are too weak to detect at the 1 ppm level. None of the bands observed here lies sufficiently close to any of the optical diffuse interstellar bands to provide positive identification.