It is shown that radicals produced from ethanol, formate, and methanol by OH radical attack are able to destroy the thymine chromophore, with a rate constant of the order of $10^{5}\ M^{-1}\,{\rm sec}^{-1}$ . Addition of small quantities of cysteine protects thymine almost completely. This is explained by H-atom transfer from the sulfhydryl compound to the organic radical thus restoring the parent organic molecule and preventing the reaction of the organic radical with thymine. It is suggested that this type of indirect protection of a DNA constituent may be of importance for the radioprotection of DNA in living cells.