Anti‐cancer drugs often increase reactive oxygen species (ROS) and cause DNA damage. Here, we highlight a new cross talk between chronic oxidative stress and the histone variant H2AX, a key player in DNA repair. We observe that persistent accumulation of ROS, due to a deficient JunD‐/Nrf2‐antioxidant response, reduces H2AX protein levels. This effect is mediated by an enhanced interaction of H2AX with the E3 ubiquitin ligase RNF168, which is associated with H2AX poly‐ubiquitination and promotes its degradation by the proteasome. ROS‐mediated H2AX decrease plays a crucial role in chemosensitivity. Indeed, cycles of chemotherapy that sustainably increase ROS reduce H2AX protein levels in Triple‐Negative breast cancer (TNBC) patients. H2AX decrease by such treatment is associated with an impaired NRF2‐antioxidant response and is indicative of the therapeutic efficiency and survival of TNBC patients. Thus, our data describe a novel ROS‐mediated regulation of H2AX turnover, which provides new insights into genetic instability and treatment efficacy in TNBC patients. Synopsis This work gives new insights into the regulation of H2AX protein turnover under chronic oxidative stress that affects DNA damage response. H2AX degradation upon chronic stress sensitizes tumour cells to chemotherapy and is indicative of better survival in triple‐negative breast cancer patients. Physiological conditions of chronic oxidative stress, mediated by the loss of JunD or Nrf2 transcription factors, are associated with a reduced protein level of the histone variant H2AX. Under conditions of chronic stress due to junD or Nrf2 deficiency, H2AX protein is targeted for degradation by the proteasome. ROS‐dependent H2AX degradation is mediated by enhanced interaction of H2AX protein with the E3 ubiquitin ligase RNF168. H2AX decrease by chronic oxidative stress increases tumour cell genomic instability and death. Chemosensitivity and survival of triple‐negative breast cancer patients are improved by stress‐mediated H2AX degradation following successive cycles of chemotherapy. This work gives new insights into the regulation of H2AX protein turnover under chronic oxidative stress that affects DNA damage response. H2AX degradation upon chronic stress sensitizes tumour cells to chemotherapy and is indicative of better survival in triple‐negative breast cancer patients.