The lack of targeted therapies for triple-negative breast cancer (TNBC) contributes to their high mortality rates and high risk of relapse compared to other subtypes of breast cancer. Most TNBCs (75%) have downregulated the expression of CREB3L1 (cAMP-responsive element binding protein 3 like 1), a transcription factor and metastasis suppressor that represses genes that promote cancer progression and metastasis. In this report, we screened an FDA-approved drug library and identified four drugs that were highly cytotoxic towards HCC1806 CREB3L1-deficient TNBC cells. These four drugs were: (1) palbociclib isethionate, a CDK4/6 inhibitor, (2) lanatocide C (also named isolanid), a Na+/K+-ATPase inhibitor, (3) cladribine, a nucleoside analog, and (4) homoharringtonine (also named omacetaxine mepesuccinate), a protein translation inhibitor. Homoharringtonine consistently showed the most cytotoxicity towards an additional six TNBC cell lines (BT549, HCC1395, HCC38, Hs578T, MDA-MB-157, MDA-MB-436), and several luminal A breast cancer cell lines (HCC1428, MCF7, T47D, ZR-75-1). All four drugs were then separately evaluated for possible synergy with the chemotherapy agents, doxorubicin (an anthracycline) and paclitaxel (a microtubule stabilizing agent). A strong synergy was observed using the combination of homoharringtonine and paclitaxel, with high cytotoxicity towards TNBC cells at lower concentrations than when each was used separately.