Abstract
Symmetrically coupled identical oscillators were once believed to support only totally synchronous or totally asynchronous states. More recently, chimera states, in which a subset of oscillators behaves coherently while the other subset exhibits disorder, have been found in large arrays of oscillators, coupled either locally or globally. We demonstrate for the first time the existence of a chimera state with only two diffusively coupled identical oscillators, one behaving nearly periodically (coherently) and the other chaotically (incoherently). We attribute this behavior to a "master-slave" interaction, which arises via a symmetry-breaking canard explosion.