A phase-separated, liquid-like organelle called the pyrenoid mediates CO2 fixation in the chloroplasts of nearly all eukaryotic algae. While most algae have 1 pyrenoid per chloroplast, here we describe a mutant in the model alga Chlamydomonas that has on average 10 pyrenoids per chloroplast. Characterization of the mutant leads us to propose a model where multiple pyrenoids are favored by an increase in the surface area of the starch sheath that surrounds and binds to the liquid-like pyrenoid matrix. We find that the mutant's phenotypes are due to disruption of a gene, which we call StArch Granules Abnormal 1 (SAGA1) because starch sheath granules, or plates, in mutants lacking SAGA1 are more elongated and thinner than those of wild type. SAGA1 contains a starch binding motif, suggesting that it may directly regulate starch sheath morphology. SAGA1 localizes to multiple puncta and streaks in the pyrenoid and physically interacts with the small and large subunits of the carbon-fixing enzyme Rubisco (ribulose-1,5-bisphosphate carboxylase/oxygenase), a major component of the liquid-like pyrenoid matrix. Our findings suggest a biophysical mechanism by which starch sheath morphology affects pyrenoid number and CO2-concentrating mechanism function, advancing our understanding of the structure and function of this biogeochemically important organelle. More broadly, we propose that the number of phase-separated organelles can be regulated by imposing constraints on their surface area.