How might nonverbal synchrony naturally evolve in a social virtual reality environment? And how can avatar embodiment affect how participants coordinate nonverbally with each other? In the following pre-registered between-subjects experiment, we tracked the movements of pairs of users during a collaborative or competitive task in immersive virtual reality. Each conversational partner controlled either a customized avatar body or an abstract cube that responded to their movements. We compared the movements of the actual user pairs between the two conditions, and to an artificial “pseudosynchrony” dataset composed of the movements of randomly combined participant pairs who did not actually interact. We found stronger positive and negative correlations between real pairs compared to pseudosynchronous pairs, providing evidence for naturally occurring nonverbal synchrony between pairs in virtual reality. We discuss this in the context of the relationships between avatar appearance, task success, social closeness and social presence.