The rotationally resolved spectrum of the A^1Π_u ← X^1Σ^+_g 000-000 transition of C_3, centered at 4051.6 Å, has been observed along 10 translucent lines of sight. To interpret these spectra, a new method for the determination of column densities and analysis of excitation profiles involving the simulation and fitting of observed spectra has been developed. The populations of lower rotational levels (J ≤ 14) in C_3 are best fitted by thermal distributions that are consistent with the kinetic temperatures determined from the excitation profile of C_2. Just as in the case of C_2, higher rotational levels (J > 14) of C_3 show increased nonthermal population distributions in clouds that have been determined to have total gas densities below ~500 cm^(-3)
