During the tumorigenic process, cancer cells may become overly dependent on the activity of backup cellular pathways for their survival, representing vulnerabilities that could be exploited as therapeutic targets. Certain molecular vulnerabilities manifest as a synthetic lethality relationship, and the identification and characterization of new synthetic lethal interactions may pave the way for the development of new therapeutic approaches for human cancer. Our goal was to investigate a possible synthetic lethal interaction between a member of the Chromodomain Helicase DNA binding proteins family (CHD4) and a member of the histone methyltransferases family (SETDB1) in the molecular context of a cell line (Hs578T) representing the triple negative breast cancer (TNBC), a subtype of breast cancer lacking validated molecular targets for treatment. Therefore, we employed the CRISPR-Cas9 gene editing tool to individually or simultaneously introduce indels in the genomic loci corresponding to the catalytic domains of SETDB1 and CHD4 in the Hs578T cell line. Our main findings included: a) introduction of indels in exon 22 of SETDB1 sensitized Hs578T to the action of the genotoxic chemotherapy doxorubicin; b) by sequentially introducing indels in exon 22 of SETDB1 and exon 23 of CHD4 and tracking the percentage of the remaining wild-type sequences in the mixed cell populations generated, we obtained evidence of the existence of a synthetic lethality interaction between these genes. Considering the lack of molecular targets in TNBC, our findings provided valuable insights for development of new therapeutic approaches not only for TNBC but also for other cancer types.