Research investigating the dynamics of coupled physical systems has demonstrated that small feedback delays can allow a dynamic response system to anticipate chaotic behavior. This counterintuitive phenomenon, termed anticipatory synchronization, has been observed in coupled electrical circuits, laser semi-conductors, and artificial neurons. Recent research indicates that the same process might also support the ability of humans to anticipate the occurrence of chaotic behavior in other individuals. Motivated by this latter work, the current study examined whether the process of feedback delay induced anticipatory synchronization could be employed to develop an interactive artificial agent capable of anticipating chaotic human movement. Results revealed that incorporating such delays within the movement-control dynamics of an artificial agent not only enhances an artificial agent's ability to anticipate chaotic human behavior, but to synchronize with such behavior in a manner similar to natural human-human anticipatory synchronization. The implication of these findings for the development of human-machine interaction systems is discussed.