Newton and LaPlace thought of the solar system as a giant clockwork. However, in the last fifteen years, theoretical studies by Jack Wisdom, experimental observations by James Klavetter, and data from the Voyager spacecraft strongly suggest that there is chaos in the clockwork: Hyperion, a tiny moon of Saturn, appears to tumble chaotically in its orbit due to its irregular shape and the nearby influence of the giant moon Titan. Our research seeks to elucidate this chaos by demonstrating its existence in the simplest possible model. We represent Hyperion by a dumbbell whose center moves along a fixed circular track. Saturn and Titan gravitationally influence Hyperion but not vice versa. Using [the custom Macintosh application] Hyperion Jr., we have demonstrated that both Titan's mass and its distance from Hyperion are essential ingredients to cause Hyperion's chaotic tumbling.