In his conversation with the Samaritan Woman, Jesus says, “If thou knewest the gift of God, and who it is that saith to thee, Give me to drink; thou wouldest have asked of him, and he would have given thee living water” (Jn 4:10). There’s a long tradition of glossing the phrase “gift of God” in this passage as the Holy Spirit — why? Notice that the Jesus mentions first God’s gift, and himself as speaker, and then goes on to mention himself again as the giver of living water — the gift of God, it appears, is exactly Jesus’ gift of living water. But what’s that? Well, if we read on in the Gospel, we find Jesus returning again to this topic, this time with an editorial gloss: “He that believeth on me, as the scripture hath said, out of his belly shall flow rivers of living water. (But this spake he of the Spirit, which they that believe on him should receive: for the Holy Ghost was not yet given; because that Jesus was not yet glorified.)” (Jn 7:38). The Spirit is the living water which is the Gift of God.
This Johannine connection finds a canonical echo in the Books of Acts. When Simon Magus offers to pay St. Peter in exchange for the Holy Spirit (8:19), Peter rebukes him: “Thy money perish with thee, because thou hast thought that the gift of God may be purchased with money” (8:20).
Why is the phrase “gift of God” appropriated to the Spirit? Augustine likes this expression for its relationality: “Holy Spirit” implies no relation to the other Triune Persons, but there can be no gift without a giver — the Spirit as Gift implies the Father (and perhaps the Son) as giver. Moreover, language of the gift leads naturally to language of the Spirit as the “bond of love” between Father and Son: the Spirit isn’t simply, Augustine suggests, the Father’s gift to us, but also the gift of the Father for the Son, and of the Son for the Father, a loving gift, and indeed a gift of love (cf. 1 Jn 4:7-8).