Chromosomal abnormalities are presented in an untreated patient with chronic myelocytic leukemia which is unusually slow in its progression. These abnormalities consist of (1) the constant presence of a subterminal chromosome longer than any of the normal complement of autosomes, (2) the presence of a Ph1 chromosome in most of these cells, and (3) consistent euploidy without diploidy. In addition, there is the puzzling inconsistency in the pair lacking one chromosome, which phenomenon maintains euploidy in spite of the single abnormal chromosomes and the equally puzzling fact that the acrocentrics both large and small are quantitatively normal in all cells counted.