Chemotaxis, the guided motion of cells by chemical gradients, plays a crucial role in many biological processes. In the social amoeba Dictyostelium discoideum, chemotaxis is critical for the formation of cell aggregates during starvation. The cells in these aggregates generate a pulse of the chemoattractant, cyclic adenosine 3,5-monophosphate (cAMP), every 6 min to 10 min, resulting in surrounding cells moving toward the aggregate. In addition to periodic pulses of cAMP, the cells also secrete phosphodiesterase (PDE), which degrades cAMP and prevents the accumulation of the chemoattractant. Here we show that small aggregates of Dictyostelium can disperse, with cells moving away from instead of toward the aggregate. This surprising behavior often exhibited oscillatory cycles of motion toward and away from the aggregate. Furthermore, the onset of outward cell motion was associated with a doubling of the cAMP signaling period. Computational modeling suggests that this dispersal arises from a competition between secreted cAMP and PDE, creating a cAMP gradient that is directed away from the aggregate, resulting in outward cell motion. The model was able to predict the effect of PDE inhibition as well as global addition of exogenous PDE, and these predictions were subsequently verified in experiments. These results suggest that localized degradation of a chemoattractant is a mechanism for morphogenesis.