We consider an agent-based predator-prey model in a two-dimensionalcontinuum space and show that a cooperative chasing strategy can emergein a social dilemma.Predators can use two different chasing strategies: A direct chasingstrategy(DCS) and a group chasing strategy (GCS).The DCS is a selfish strategy with which a chaser moves straighttoward the nearest prey, and the GCS is a cooperative strategy in thesense that the chaser chooses the chasing direction for the group at acost of its own speed.A prey flees away from the nearest hazard, either a chaser or theboundary, within its recognition range.We check the capturing activities of each strategy and find a socialdilemma between the two strategies because the GCS is more efficientfor the group whereas the DCS is better individually.Using a series of numerical simulations, we further show that thecooperative strategy can proliferate when a learning process of nearbysuccessful strategies is introduced.