Coordination of growth and division in eukaryotic cells is essential for populations of proliferating cells to maintain size homeostasis, but the underlying mechanisms that govern cell size have only been investigated in a few taxa. The green alga Chlamydomonas reinhardtii (Chlamydomonas) proliferates using a multiple fission cell cycle that involves a long G1 phase followed by a rapid series of successive S and M phases (S/M) that produces 2n daughter cells. Two control points show cell-size dependence: Commitment in mid-G1 phase requires attainment of a minimum size to enable at least one mitotic division during S/M, and the S/M control point where mother cell size governs cell division number (n), ensuring that daughter distributions are uniform. tny1 mutants pass Commitment at a smaller size than wild type and undergo extra divisions during S/M phase to produce small daughters, indicating that TNY1 functions to inhibit size-dependent cell cycle progression. TNY1 encodes a cytosolic hnRNP A-related RNA binding protein and is produced once per cell cycle during S/M phase where it is apportioned to daughter cells, and then remains at constant absolute abundance as cells grow, a property known as subscaling. Altering the dosage of TNY1 in heterozygous diploids or through overexpression increased Commitment cell size and daughter cell size, indicating that TNY1 is a limiting factor for both size control checkpoints. Epistasis placed TNY1 function upstream of the retinoblastoma tumor suppressor complex (RBC) and one of its regulators, Cyclin-Dependent Kinase G1 (CDKG1). Moreover, CDKG1 protein and mRNA were found to over-accumulate in tny1 cells suggesting that CDKG1 may be a direct target of repression by TNY1. Our data expand the potential roles of subscaling proteins outside the nucleus and imply a control mechanism that ties TNY1 accumulation to pre-division mother cell size.