Sonoluminescence (SL) is generated from single, stably oscillating bubbles in a stationary, time-periodic acoustic field. By measuring the time delay between flashes, the dynamics of the phenomenon has been investigated. While other researchers have concentrated on the remarkable periodic stability of the system, present results indicate that, for small variations in the governing parameters, period doubling, chaos, and quasiperiodicity can occur. The implications of the complex temporal behavior for the problem of determining the mechanism(s) for production of SL are discussed. Approved for public release; distribution is unlimited. Work was done with partial support from NASA, Office of Naval Research and the Naval Postgraduate School research program, and Deutsche Forschungsgemeinscchaft