Recent studies showed that Fatty Acid Synthase (FASN), a lipogenic enzyme overexpressed in several carcinomas, plays an important role in drug resistance. Furthermore, the enrichment of Breast Cancer Stem Cell (BCSC) features has been found in breast tumors that progressed after chemotherapy. Hence, we used the triple negative breast cancer (TNBC) cell line MDA-MB-231 (231) to evaluate the FASN and BCSC population role in resistance acquisition to chemotherapy. For this reason, parental cell line (231) and its derivatives resistant to doxorubicin (231DXR) and paclitaxel (231PTR) were used. The Mammosphere-Forming Assay and aldehyde dehydrogenase (ALDH) enzyme activity assay showed an increase in BCSCs in the doxorubicin-resistant model. Moreover, the expression of some transcription factors involved in epithelial-mesenchymal transition (EMT), a process that confers BCSC characteristics, was upregulated after chemotherapy treatment. FASN inhibitors C75, (−)-Epigallocatechin 3-gallate (EGCG), and its synthetic derivatives G28, G56 and G37 were used to evaluate the effect of FASN inhibition on the BCSC-enriched population in our cell lines. G28 showed a noticeable antiproliferative effect in adherent conditions and, interestingly, a high mammosphere-forming inhibition capacity in all cell models. Our preliminary results highlight the importance of studying FASN inhibitors for the treatment of TNBC patients, especially those who progress after chemotherapy.