Solutions of cyclohexane, chlorine, and sulfur dioxide in carbon tetrachloride were irrodioted in on oxygen-free system with gamma rays from uranium fission products contained in spent fuel elements. Reaction rates, equivalent to the rate of disappearance of free chlorine, were determined spectrophotometrically a t 4,000A. The reaction products were cyclohexanesulfonyl chloride and hydrochloric acid in nearly stoichiometric quantities. An empirical rate equation was derived, in which the rate of disappea:ance of chlorine was shown to be proportional to the square root of the product of absorbed radiotion, chlorine and cyclohexane concentrations, and independent of the concentration of sulfur dioxide. A chain mechanism was proposed, ond the rate equation derived from this scheme was found to be in excellent agreement with the empirical rate equation. The reaction proceeded by a free radical mechanism, 0s evidenced by the strong inhibiting effect of oxygen. G numbers were of the order of 105, corresponding to an estimated chain length of 5,000, which is of the same order as the quantum yield of the photochemical sulfochlorination.