The recently discovered human lncRNA NORAD is induced after DNA damage in a p53-dependent manner. It plays a critical role in the maintenance of genomic stability through interaction with Pumilio proteins, limiting the repression of their target mRNAs. Therefore, NORAD inactivation causes chromosomal instability and aneuploidy, which contributes to the accumulation of genetic abnormalities and tumorigenesis. NORAD has been detected in several types of cancer, including breast cancer, which is the most frequently diagnosed and the second-leading cause of cancer death in women. In the present study, we confirmed upregulated NORAD expression levels in a set of human epithelial breast cancer cell lines (MDA-MB-231, MDA-MB-436, and MDA-MB-468), which belong to the most aggressive subtypes (triple-negative breast cancer). These results are in line with previous data showing that high NORAD expression levels in basal-like tumors were associated with poor prognosis. Here, we demonstrate that NORAD downregulation sensitizes triple-negative breast cancer cells to chemotherapy, through a potential accumulation of genomic aberrations and an impaired capacity to signal DNA damage. These results show that NORAD may represent an unexploited neoadjuvant therapeutic target for chemotherapy-unresponsive breast cancer.