Many stem cells undergo asymmetric division to produce a self-renewing stem cell and a differentiating daughter cell. Here we show that, similarly to H3, histone H4 is inherited asymmetrically in Drosophila melanogaster male germline stem cells undergoing asymmetric division. In contrast, both H2A and H2B are inherited symmetrically. By combining super-resolution microscopy and chromatin fiber analyses with proximity ligation assays on intact nuclei, we find that old H3 is preferentially incorporated by the leading strand, whereas newly synthesized H3 is enriched on the lagging strand. Using a sequential nucleoside analog incorporation assay, we detect a high incidence of unidirectional replication fork movement in testes-derived chromatin and DNA fibers. Biased fork movement coupled with a strand preference in histone incorporation would explain how asymmetric old and new H3 and H4 are established during replication. These results suggest a role for DNA replication in patterning epigenetic information in asymmetrically dividing cells in multicellular organisms.