The flagellated protozoan Salpingoeca rosetta is one of the closest relatives of multicellular animals. Unicellular S. rosetta can be induced to form multicellular colonies, but colonies swim more slowly than individual cells so the advantages conferred by colony formation are uncertain. Here we use theoretical models to show that hydrodynamic cooperation between cells can increase the fluid supply to the colony, an important predictor of feeding rate. Our results suggest that hydrodynamic benefits may have been an important selective factor in the evolution of early multicellular animals.