Despite the big increase in precision medicine targeted therapies developing curative treatments for many cancers is still a major challenge due mainly to the development of drug resistance in cancer stem cells. The cancer stem cells are constantly evolving to survive and targeted drug treatment often increases the selective pressure on these cells from which the disease develops. Chronic myeloid leukaemia is a paradigm of cancer stem cell research. Targeted therapies to the causative oncogene, BCR/ABL, have been developed but drug resistance remains a problem. The introduction of tyrosine kinase inhibitors targeting BCR/ABL were transformative in the management of CML. However, patients are rarely cured as the tyrosine kinase inhibitors fail to eradicate the leukaemic stem cell which often leads to loss of response to therapy as drug resistance develops and progression to more fatal forms of acute leukaemia occurs. New treatment strategies targeting other entities within the leukemic stem cell either alone or in combination with tyrosine kinase are therefore required. Drawing on our previous published work on the development of potential novel targets in CML and other myeloproliferative diseases along with analysis of the facilitates chromatin transcription (FACT) complex in CML we hypothesised that curaxin, a drug that targets the FACT complex and is in clinical trial for the treatment of other cancers, could be of use in the treatment of CML. We therefore assessed the curaxin CBL0137 as a new agent to extinguish CML primitive cells and show its ability to preferentially target CML cells compared to healthy control cells, especially in combination with clinically relevant tyrosine kinase inhibitors.