Most complex multicellular organisms develop clonally from a single cell. This should limit conflicts between cell lineages that could threaten the extensive cooperation of cells within multicellular bodies. Cellular composition can be manipulated in the social amoeba Dictyostelium discoideum, which allows us to test and confirm the two key predictions of this theory. Experimental evolution at low relatedness favored cheating mutants that could destroy multicellular development. However, under high relatedness, the forces of mutation and within-individual selection are too small for these destructive cheaters to spread, as shown by a mutation accumulation experiment. Thus, we conclude that the single-cell bottleneck is a powerful stabilizer of cellular cooperation in multicellular organisms.