We consider the problem of designing distributed algorithms that enable a group of agents (followers) to track a reference trajectory generated by a leader agent. Such algorithms are an integral part of a variety of distributed estimation and control techniques like the attitude control problem for spacecraft formation flying. Existing methods assume that the leader's reference dynamics are fully known to one or more follower agents, and they typically require significant amounts of inter-agent communication. In this paper, we propose a novel distributed adaptive observer in which no follower agent knows the leader's reference dynamics. In addition, our method does not require as much inter-agent communication as existing methods. We use appropriate Lyapunov functions to prove convergence, and we present numerical examples to demonstrate the efficacy of our approach.