Most eukaryotic cells execute binary division after each mass doubling in order to maintain size homeostasis by coordinating cell growth and division. By contrast, the photosynthetic green alga Chlamydomonas can grow more than 8-fold during daytime and then, at night, undergo rapid cycles of DNA replication, mitosis, and cell division, producing up to 16 daughter cells. Here, we propose a mechanistic model for multiple-fission cycles and cell-size control in Chlamydomonas. The model comprises a light-sensitive and size-dependent biochemical toggle switch that acts as a sizer, guarding transitions into and exit from a phase of cell-division cycle oscillations. This simple “sizer-oscillator” arrangement reproduces the experimentally observed features of multiple-fission cycles and the response of Chlamydomonas cells to different light-dark regimes. Our model also makes specific predictions about the size dependence of the time of onset of cell division after cells are transferred from light to dark conditions, and we confirm these predictions by single-cell experiments. Collectively, our results provide a new perspective on the concept of a “commitment point” during the growth of Chlamydomonas cells and hint at intriguing similarities of cell-size control in different eukaryotic lineages.