Reactive oxygen species (ROSs) are produced during normal cellular metabolism, particularly by respiration in mitochondria, and these ROSs are considered to cause oxidative damage to macromolecules, including DNA. In our previous paper, we found no indication that depletion of mitochondrial superoxide dismutase, SOD2, resulted in an increase in DNA damage. In this paper, we examined SOD1, which is distributed in the cytoplasm, nucleus, and mitochondrial intermembrane space. We generated conditional SOD1 knockout cells from chicken DT40 cells and analyzed their phenotypes. The results revealed that SOD1 was essential for viability and that depletion of SOD1, especially nuclear SOD1, increased sister chromatid exchange (SCE) frequency, suggesting that superoxide is generated in or near the nucleus and that nuclear SOD1 functions as a guardian of the genome. Furthermore, we found that ascorbic acid could offset the defects caused by SOD1 depletion, including cell lethality and increases in SCE frequency and apurinic/apyrimidinic sites.