I argue that the conversation in Plato’s Phaedo operates on two levels, and appeals to two different notions of immortality, one temporal (continuing life after death or before birth) and one atemporal (immunity from death, time and all sequential events). Socrates and his friends are concerned about whether the soul will survive beyond the present life, and whether it existed prior to birth. While this looks like a concern about temporal survival, I argue that Plato, as author, is identifying another kind of immortality, proper to the soul alone, as a being outside time, to which 'before' and 'after' do not apply. By examining exactly what is meant by its immunity to death (in a number of senses of ‘death’) and its association with life (in one sense of ‘life’), I consider in what sense the soul could have a kind of atemporal being akin to that which pertains to the Forms, and examine some puzzles about how such a being could enter into temporal experience in conjunction with a sequence of bodies.