Basal-like triple-negative breast cancers (TNBCs) have poor prognosis. To identify basal-like TNBC dependencies, a genome-wide siRNA lethality screen compared two human breast epithelial cell lines transformed with the same genes: basal-like BPLER and myoepithelial HMLER. Expression of the screen's 154 BPLER dependency genes correlated with poor prognosis in breast, but not lung or colon, cancer. Proteasome genes were overrepresented hits. Basal-like TNBC lines were selectively sensitive to proteasome inhibitor drugs relative to normal epithelial, luminal, and mesenchymal TNBC lines. Proteasome inhibition reduced growth of established basal-like TNBC tumors in mice and blocked tumor-initiating cell function and macrometastasis. Proteasome addiction in basal-like TNBCs was mediated by NOXA and linked to MCL-1 dependence.