Chromosome segregation typically occurs after replication has finished in eukaryotes but during replication in bacteria. Here, we show that the alphaproteobacterium Hyphomonas neptunium, which proliferates by bud formation at the tip of a stalk-like cellular extension, segregates its chromosomes in a unique two-step process. First, the two sister origin regions are targeted to opposite poles of the mother cell, driven by the ParABS partitioning system. Subsequently, once the bulk of chromosomal DNA has been replicated and the bud exceeds a certain threshold size, the cell initiates a second segregation step during which it transfers the stalk-proximal origin region through the stalk into the nascent bud compartment. Thus, while chromosome replication and segregation usually proceed concurrently in bacteria, the two processes are largely uncoupled in H. neptunium, reminiscent of eukaryotic mitosis. These results indicate that stalked budding bacteria have evolved specific mechanisms to adjust chromosome segregation to their unusual life cycle.