In standard english, one may easily read this as saying that faith is a gift. But in the original Greek, it becomes clear that this is not what Paul is saying here. The Greek word for "this" is touto, which is neuter, while the Greek word for "faith" is pistis, which is feminine. They don't agree in gender, so the "this" cannot refer to "faith". Rather, it refers to the antecedent of salvation by grace through faith. It is salvation itself that is said to be a gift, not faith. New Testament Greek scholar A. T. Robertson states:
'Grace' is God's part, 'faith' ours. And that [it] (kai touto) is neuter, not feminine taute, and so refers not to pistis [faith] or to charis [grace] (feminine also), but to the act of being saved by grace conditioned on faith on our part. (World Pictures in the New Testament, 4:525)
John Calvin agrees:
He does not mean that faith is the gift of God, but that salvation is given to us by God, or, that we obtain it by the gift of God. (Calvin's Commentaries, vol. 11, 145)