The discrete visible absorption spectrum of natural chlorine heated to 670°K, Cl 2(A 3Π(0 u+) ← X 1Σg+) , was recorded with a resolving power of 300 000. Twelve bands (5 ≤ v' ≤ 10 and 3 ≤ v″ ≤ 5) (including 10 new bands) of 35Cl 35Cl, and three new bands of 35Cl 37Cl were analyzed. The first accurate data for the vibrational levels v″ = 4 and 5, and v' = 5, and for high rotational levels ( J < 58), were obtained. Values for the centrifugal stretching constants Dv of both the 3Π(0 u+) and 1Σg+ states were measured systematically. Only two isolated perturbations (of the rotational levels v' = 8, J' = 26, and v' = 9, J' = 46) exist for the known vibrational and rotational levels of 35Cl 35Cl ( 3Π(0 u+) ). Previous data for the ground state of Cl 2 have been reinterpreted, with the assignment to the resonance emission doublet series of Jr = 21; the previous potential function for this state is incorrect. New values for the constants of Cl 2 are reported. The revised values for Bv″ alter the RKR potential curve for 35Cl 35Cl (X 1Σg+) in such a way that the previous suggestion of a strong perturbation in the ground state is untenable.