Breast cancer susceptibility gene 1 (BRCA1) is a tumor suppressor gene, which is frequently mutated in breast and ovarian cancers. BRCA1 plays a key role in the homologous recombination directed DNA repair, allowing its deficiency to act as a therapeutic target of DNA damaging agents. In this study, we found that inhibition of the class I histone deacetylases (HDAC) exhibited synthetic lethality with BRCA1 deficiency in breast cancer cells. Transcriptome profiling and validation study showed that HDAC inhibition enhanced the expression of thioredoxin interaction protein (TXNIP), causing reactive oxygen species (ROS)-mediated DNA damage. This effect induced preferential apoptosis in BRCA1 breast cancer cells where DNA repair system is compromised. Two animal experiments and gene expression-associated patients’ survival analysis further confirmed in vivo synthetic lethality between BRCA1 and HDAC. Finally, the combination of inhibitors of HDAC and bromodomain and extra-terminal motif (BET), another BRCA1 synthetic lethality target that also works through oxidative stress-mediated DNA damage, showed a strong anticancer effect in BRCA1 breast cancer cells. Together, this study provides a new therapeutic strategy for BRCA1-deficient breast cancer by targeting two epigenetic machineries, HDAC and BET.