Chlorine (Cl2) is a diatomic molecule used as an important industrial gas. However, the electron affinity (EA) of Cl2, a fundamental parameter for understanding chemical reactions, has no accurate experimental result available. The latest result of the EA value of Cl2 is 2.50(20) eV reported in 1983. In the present work, we report the precision measurement of the EA of Cl2 with the successive difference method via the high-resolution photoelectron spectroscopy of cryogenically cold chlorine anions Cl2-. The EA of Cl2 is determined to be 19432(9) cm-1 or 2.4093(11) eV.