‘There is no well-known individual in all Greek mythology except Alcestis [original emphasis] who dies and is returned to human life without cosmic repercussions which are soon remedied’ (John Heath). The ineluctability of death is not just a feature of Greek myth in general but is also one of the most prominent themes in Euripides’ version of the story in his play Alcestis (438 bc). A further problem is that Greek tragedy is a basically realistic genre which is not hospitable to violations of the laws of nature. Euripides thus set himself a remarkable challenge in Alcestis, to present an event which violates a law of nature which is so unbreakable that it is on the whole observed throughout Greek mythology as well as being repeatedly affirmed in the play. This article will examine how he succeeds in doing so in a way which is dramatically convincing.