The role of immortal DNA strands that co-segregate during mitosis of asymmetrically self-renewing distributed stem cells (DSCs) is unknown. Previously, investigation of immortal DNA strand function and molecular mechanisms responsible for their nonrandom co-segregation was precluded by difficulty in identifying DSCs and immortal DNA strands. Here, we report the use of two technological innovations, selective DSC expansion and establishment of H2A.Z chromosomal asymmetry as a specific marker of 'immortal chromosomes,' to investigate molecular properties of immortal chromosomes and opposing 'mortal chromosomes' in cultured mouse hair follicle DSCs. Although detection of the respective suppressive and activating H3K27me3 and H3K4me3 epigenetic marks on immortal chromosomes was similar to randomly segregated chromosomes, detection of both was lower on mortal chromosomes destined for lineage-committed sister cells. This global epigenomic feature of nonrandom co-segregation may reveal a mechanism that maintains an epigenome-wide 'poised' transcription state, which preserves DSC identity, while simultaneously activating sister chromosomes for differentiation.