Two ions confined to a radio-frequency trap and cooled by radiation pressure exhibit deterministic chaos. Theoretical analysis of the two-ion dynamics reveals that the route to chaos is due solely to ion-ion collisions. During a collision, the nonlinear Coulomb interaction introduces a transient instability, which gives way to stable single-particle-like motion as the ions move apart. The chaotic dynamics are characterized by a strange attractor that resembles a spiral galaxy. © 1990 Nature Publishing Group.