Aristotle (384-322 BC) talked about zoe versus psyche in his treatise De Anima ("On the Soul"). However, his concept of the mortal and immortal components of the complete human is a bit different than our current understanding.
An excerpt from the Catholic Encyclopedia discusses this:
For Aristotle, in the case of living natural bodies the vital principle, psyche is the form. His doctrine is embodied in his famous definition: psyche estin entekexeia e prote somatos fysikou dynamei zoen exontos. (De Anima, II, i), i.e. the soul is therefore the first entelechy (substantial form or perfect actualization) of a natural or organized body potentially possessing life. The definition applies to plants, animals, and man.
That source goes on to say
The human soul, however, seems to be of a different kind (genos etepron), and separable as the eternal from the perishable.
However, it should be noted that while Aristotle considers the zoe to be separable from the psyche, it's the psyche that is eternal, not the zoe:
Aristotle also argues that the mind (only the agent intellect) is immaterial, able to exist without the body, and immortal.
He holds that the soul is the form, or essence of any living thing; that it is not a distinct substance from the body that it is in; that it is the possession of soul (of a specific kind) that makes an organism an organism at all, and thus that the notion of a body without a soul, or of a soul in the wrong kind of body, is simply unintelligible.
Some commentators have suggested that Aristotle's term soul is better translated as lifeforce
Given this, I would have to say that yes, the concept that there is a mortal component and an eternal component to us all is an older concept the Christianity. However, the concept isn't quite the same as our current understanding.