We investigated positioning of chromosomes during the cell cycle in live mammalian cells with a combined experimental and computational approach. By non-invasive labeling of chromosome subsets and tracking by 4D imaging, we could show that no global rearrangements occurred in interphase. Using the same assay, we also observed a striking order of chromosomes throughout mitosis. By contrast, our computer simulation based on stochastic movements of individual chromosomes predicted randomization of chromosome order in mitosis. In vivo, a quantitative assay for single chromosome positioning during mitosis revealed strong similarities between daughter and mother cells. These results demonstrate that global chromosome positions are heritable through the cell cycle in mammalian cells. Based on tracking of labeled chromosomes and centromeres during chromosome segregation and experimental perturbations of chromosomal order, we propose that chromosome specific timing of sister chromatid separation transmits chromosomal positions from one cell generation to the next.