Chronic myeloid leukemia (CML) is an acquired neoplastic hematopoietic stem cell (HSC) disorder characterized by the expression of the BCR-ABL oncoprotein. This gene product is necessary and sufficient to explain the chronic phase of CML. The only known cause of CML is radiation exposure leading to a mutation of at least one HSC, although the vast majority of patients with CML do not have a history of radiation exposure. Nonetheless, in humans, significant radiation exposure (after exposure to atomic bomb fallout) leads to disease diagnosis in 3-5 years. In murine models, disease dynamics are much faster and CML is fatal over the span of a few months. Our objective is to develop a model that accounts for CML across all mammals. In the following, we combine a model of CML dynamics in humans with allometric scaling of hematopoiesis across mammals to illustrate the natural history of chronic phase CML in various mammals. We show how a single cell can lead to a fatal illness in mice and humans but a higher burden of CML stem cells is necessary to induce disease in larger mammals such as elephants. The different dynamics of the disease is rationalized in terms of mammalian mass. Our work illustrates the relevance of animal models to understand human disease and highlights the importance of considering the re-scaling of the dynamics that accrues to the same biological process when planning experiments involving different species.