Understanding of the visual system can be informed by examining errors in perception. We present a novel illusion-Wandering Circles-in which stationary circles undergoing contrast-polarity reversals (i.e., flicker), when viewed peripherally, appear to move about in a random fashion. In two psychophysical experiments, participants rated the strength of perceived illusory motion under varying stimulus conditions. The illusory motion percept was strongest when the circle's edge was defined by a light/dark alternation and when the edge faded smoothly to the background gray (i.e., a circular arrangement of the Craik-O'Brien-Cornsweet illusion). In addition, the percept of illusory motion is flicker rate dependent, appearing strongest when the circles reversed polarity 9.44 times per second and weakest at 1.98 times per second. The Wandering Circles differ from many other classic motion illusions as the light/dark alternation is perfectly balanced in time and position around the edges of the circle, and thus, there is no net directional local or global motion energy in the stimulus. The perceived motion may instead rely on factors internal to the viewer such as top-down influences, asymmetries in luminance and motion perception across the retina, adaptation combined with positional uncertainty due to peripheral viewing, eye movements, or low contrast edges.