In many respects, Rhesus is an unparalleled oddity. Attributed to Euripides, it was (probably) composed in the fourth century BC by a now anonymous poet, and thus (probably) constitutes our only extant fourth-century tragedy. Unlike any other surviving tragedy, it dramatizes an episode narrated in the Iliad and is set wholly at night. It features a fourth speaking actor. Other highlights include a chase scene, Athena imitating Aphrodite's voice, and the only singing goddess (the Muse) in extant tragedy. Such is Rhesus, the strangest, most maligned, least understood of tragedies. In this article, I reconsider one comparatively neglected anomaly among many: the use or otherwise of the stage building.