Accurate chromosome segregation during eukaryotic cell division requires a microtubule spindle, formation of which in animals is driven by centrosomes. To maintain genome stability, centrosomes must be duplicated once every cell division cycle along with the genomic DNA. Hemerly et al. show that Orc1, a component of the origin recognition complex (ORC) essential for DNA replication, also acts at centrosomes to control their copy number. Orc1 inhibits Cyclin E–dependent reduplication of the centrosome, and its localization to centrosomes is directed by the Orc1-binding partner Cyclin A.