Centromeres are epigenetically defined by CENP-A-containing chromatin and are essential for cell division. Previous studies suggest asymmetric inheritance of centromeric proteins upon stem cell division; however, the mechanism and implications of selective chromosome segregation remain unexplored. We show that Drosophila female germline stem cells (GSCs) and neuroblasts assemble centromeres after replication and before segregation. Specifically, CENP-A deposition is promoted by CYCLIN A, while excessive CENP-A deposition is prevented by CYCLIN B, through the HASPIN kinase. Furthermore, chromosomes inherited by GSCs incorporate more CENP-A, making stronger kinetochores that capture more spindle microtubules and bias segregation. Importantly, symmetric incorporation of CENP-A on sister chromatids via HASPIN knockdown or overexpression of CENP-A, either alone or together with its assembly factor CAL1, drives stem cell self-renewal. Finally, continued CENP-A assembly in differentiated cells is nonessential for egg development. Our work shows that centromere assembly epigenetically drives GSC maintenance and occurs before oocyte meiosis.