In this paper I would like to examine a conception of happiness that seems to have become popular after the time of Plato and Aristotle: tranquillity or, as one might also say, peace of mind. This conception is interesting for two reasons: first, because it seems to come from outside the tradition that began with Plato or Socrates, second, because it is the only conception of eudaimonia in Greek ethics that identifies happiness with a state of mind and makes it depend entirely on a person's attitude or beliefs. In this way it may be closer to more recent ideas about happiness, notably those of utilitarians who treat “happiness” as a synonym of “pleasure,” than to the classical Greek conceptions of the good life. For Plato and Aristode (and in fact for the Hellenistic philosophers too, including the hedonist Epicurus) the happy life certainly had to be pleasant or enjoyable, but they did not think that happiness itself consisted in being pleased with one's life. As the (somewhat unorthodox) Stoic Seneca puts it, “it is not that virtue is chosen because it pleases, but that, if chosen, it also pleases.” I will argue that tranquillity was in fact not a serious contender for the position of ultimate good in ancient times. Greek theories of happiness from Plato to Epicurus were attempts to spell out what sort of a life one would have to lead in order to have good reasons for feeling tranquil or contented; they were not recipes for reaching a certain state of mind.