The search is ongoing for new anticancer therapeutics that would overcome resistance to chemotherapy. This includes chronic myeloid leukemia, particularly suitable for the studies of novel anticancer compounds due to its homogenous and well-known genetic background. Here we show anticancer efficacy of novel dicarboximide denoted BK124.1 (C31H37ClN2O4) in a mouse CML xenograft model and in vitro in two types of chemoresistant CML cells: MDR1 blasts and in CD34+ patients’ stem cells (N = 8) using immunoblotting and flow cytometry. Intraperitoneal administration of BK124.1 showed anti-CML efficacy in the xenograft mouse model (N = 6) comparable to the commonly used imatinib and hydroxyurea. In K562 blasts, BK124.1 decreased the protein levels of BCR-ABL1 kinase and its downstream effectors, resulting in G2/M cell cycle arrest and apoptosis associated with FOXO3a/p21waf1/cip1 upregulation in the nucleus. Additionally, BK124.1 evoked massive apoptosis in multidrug resistant K562-MDR1 cells (IC50 = 2.16 μM), in CD34+ cells from CML patients (IC50 = 1.5 µM), and in the CD34+/CD38− subpopulation consisting of rare, drug-resistant cancer initiating stem cells. Given the advantages of BK124.1 as a potential chemotherapeutic and its unique ability to overcome BCR-ABL1 dependent and independent multidrug resistance mechanisms, future development of BK124.1 could offer a cure for CML and other cancers resistant to present drugs.