Apicomplexan parasites undergo cell division using an evolutionarily conserved mechanism first described in the positioning and assembly of flagella in algae., Apicomplexa are intracellular parasites that cause important human diseases including malaria and toxoplasmosis. During host cell infection new parasites are formed through a budding process that parcels out nuclei and organelles into multiple daughters. Budding is remarkably flexible in output and can produce two to thousands of progeny cells. How genomes and daughters are counted and coordinated is unknown. Apicomplexa evolved from single celled flagellated algae, but with the exception of the gametes, lack flagella. Here we demonstrate that a structure that in the algal ancestor served as the rootlet of the flagellar basal bodies is required for parasite cell division. Parasite striated fiber assemblins (SFA) polymerize into a dynamic fiber that emerges from the centrosomes immediately after their duplication. The fiber grows in a polarized fashion and daughter cells form at its distal tip. As the daughter cell is further elaborated it remains physically tethered at its apical end, the conoid and polar ring. Genetic experiments in Toxoplasma gondii demonstrate two essential components of the fiber, TgSFA2 and 3. In the absence of either of these proteins cytokinesis is blocked at its earliest point, the initiation of the daughter microtubule organizing center (MTOC). Mitosis remains unimpeded and mutant cells accumulate numerous nuclei but fail to form daughter cells. The SFA fiber provides a robust spatial and temporal organizer of parasite cell division, a process that appears hard-wired to the centrosome by multiple tethers. Our findings have broader evolutionary implications. We propose that Apicomplexa abandoned flagella for most stages yet retained the organizing principle of the flagellar MTOC. Instead of ensuring appropriate numbers of flagella, the system now positions the apical invasion complexes. This suggests that elements of the invasion apparatus may be derived from flagella or flagellum associated structures., Author Summary Malaria, toxoplasmosis, and related diseases are caused by infection with unicellular parasites called Apicomplexa. Their name refers to the elaborate invasion machinery that occupies the apical end of the parasite cell. This apparatus allows the parasite to force its way into the cells of its host, and to deliver factors that will manipulate host cell structure, gene expression, and metabolism. Once in the host cell the parasite will begin to grow. The parasite replicates its genome and organelles numerous times and then loads these various elements into numerous daughter cells that will further spread the infection. Here we report a fiber that coordinates the daughter cell budding process. The fiber links the centrosome, which controls the mitotic spindle, and the genome with the microtubule organizing center of the budding daughter. Parasite mutants lacking the proteins that build the fiber fail to form daughter cells at the earliest step. The fiber and its components are remarkably similar to fibers that coordinate flagella in algae. While Apicomplexa are not flagellated (with the exception of certain gamete stages) they evolved from flagellated algae. We propose that elements of the invasion apparatus evolved from the flagellum or flagellum associated structures.