Breast cancer, the most frequent cancer in women, is generally classified into several distinct histological and molecular subtypes. However, single-cell technologies have revealed remarkable cellular and functional heterogeneity across subtypes and even within individual breast tumors. Much of this heterogeneity is attributable to dynamic alterations in the epigenetic landscape of the cancer cells, which promote phenotypic plasticity. Such plasticity, including transition from luminal to basal-like cell identity, can promote disease aggressiveness. We now report that the tumor suppressor LATS1, whose expression is often downregulated in human breast cancer, helps maintain luminal breast cancer cell identity by reducing the chromatin accessibility of genes that are characteristic of a “basal-like” state, preventing their spurious activation. This is achieved via interaction of LATS1 with the NCOR1 nuclear corepressor and recruitment of HDAC1, driving histone H3K27 deacetylation near NCOR1-repressed “basal-like” genes. Consequently, decreased expression of LATS1 elevates the expression of such genes and facilitates slippage towards a more basal-like phenotypic identity. We propose that by enforcing rigorous silencing of repressed genes, the LATS1-NCOR1 axis maintains luminal cell identity and restricts breast cancer progression.