This paper describes a robotic system that uses dance as a form of social interaction to explore the properties and importance of rhythmic movement in general social interaction. The system consists of a small creature-like robot whose movement is controlled by a rhythm-based software system. Environmental rhythms can be extracted from auditory or visual sensory stimuli, and the robot synchronizes its movement to a dominant rhythm. The system was demonstrated, and an exploratory study conducted, with children interacting with the robot in a generalized dance task. Through a behavioral analysis of videotaped interactions, we found that the robot's synchronization with the background music had an effect on children's interactive involvement with the robot. Furthermore, we observed a number of expected and unexpected styles and modalities of interactive exploration and play that inform our discussion on the next steps in the design of a socially rhythmic robotic system.