Chronic myeloid leukemia (CML) is sustained by a rare population of primitive, quiescent, BCR-ABL⁺ cells and represents an excellent example of a malignancy in which tumor-initiating cells represent the key to disease eradication. CML is also the first malignancy for which targeted therapy has replaced conventional chemotherapy. Within a vast excess of proliferating progenitor cells that express breakpoint cluster region-abelson (BCR-ABL) and are exquisitely sensitive to the tyrosine kinase inhibitor imatinib mesylate (IM) resides a small population of quiescent leukemic cells that, despite higher levels of BCR-ABL transcripts, exhibits innate insensitivity to IM. These cells remain after IM therapy, even when apparently complete responses are achieved, and they probably explain molecular disease persistence. Although it can be argued that patients may survive for many years with low levels of leukemia still present, it is possible to achieve disease clearance at the molecular level following an allogeneic stem cell transplantation. The emergence of drug resistance with IM monotherapy also argues in favor of complete disease eradication that we believe should remain the ultimate therapeutic goal in CML. New approaches to the elimination of these primitive CML cells may thus be crucial to the development of curative strategies.