The article describes an accessible example of dynamical chaos which has been discussed recently in the Journal of Physics. It is simple enough to be explored by microcomputer at home or school. It concerns a point “billiard ball” bouncing round an ideal square “billiard table” that rotates steadily. Without rotation the ball's motion would be a perfectly regular sequence of straight-line transits; with rotation most of the motion is unpredictably jumbled—chaotic, as we'll see. First some simple theory is needed.