Most patients with advanced triple-negative breast cancer (TNBC) develop drug resistance. MYC and MCL1 are frequently co-amplified in drug-resistant TNBC after neoadjuvant chemotherapy. Herein, we demonstrate that MYC and MCL1 cooperate in the maintenance of chemotherapy-resistant cancer stem cells (CSCs) in TNBC. MYC and MCL1 increased mitochondrial oxidative phosphorylation (mtOXPHOS) and the generation of reactive oxygen species (ROS), processes involved in maintenance of CSCs. A mutant of MCL1 that cannot localize in mitochondria reduced mtOXPHOS, ROS levels, and drug-resistant CSCs without affecting the anti-apoptotic function of MCL1. Increased levels of ROS, a by-product of activated mtOXPHOS, led to the accumulation of HIF-1α. Pharmacological inhibition of HIF-1α attenuated CSC enrichment and tumor initiation in vivo. These data suggest that (1) MYC and MCL1 confer resistance to chemotherapy by expanding CSCs via mtOXPHOS and (2) targeting mitochondrial respiration and HIF-1α may reverse chemotherapy resistance in TNBC. MYC and MCL1 are co-amplified in drug-resistant breast cancer. Lee et al. reveal that MYC and MCL1 cooperate to maintain cancer stem cells (CSCs) resistant to chemotherapy by increasing mitochondrial OXPHOS, ROS production, and HIF-1α expression. Inhibition of HIF-1α blocks CSC expansion and restores chemotherapy sensitivity.