We describe an experiment which takes advantage of the surprising complexity of one of the simplest physical systems, the passive double pendulum. For large angle swings sensitive dependence on initial conditions, the signature of chaos, may be demonstrated and quantified in a very direct way. Small angle experiments and zero gravity experiments (with the pendulum swinging in a horizontal plane) may also be performed. The angles are measured very precisely and reliably using optical encoder wheels, and data are acquired and displayed using a personal computer. The experiment is suitable for the undergraduate laboratory.