This article returns to the question of the “third” in gift literature starting with the given object which opens the gift cycle. Having shown how the quaternary structure of the Oedipus as conceived by Jacques Lacan rests on Lévi-Strauss’“kinship particle, ” we present a more maussian side of Lacan who moves away from Lévi-Strauss’“exchange of women” while introducing the notion of “phallus.” We can thus see that the immanence of the figure of the third in symbolic expression (and thus to the gift) can be elucidated in light of the lacanian theory of the “missing-object” which Lacan derived from his reading of Mauss’ Essay on Gift. We thus propose there is an unconscious dimension of gift which is constitutively open.