No, I am not saying that John Chrysostom held to a reformed view of the atonement of our Lord Jesus Christ. After all, he was, to be sure, an Antiochian exegete of his day, which by and large excluded being open to our exegetical and theological perspectives. But he does, in this instance, affirm unwittingly a limited atonement... Chrysostom (349-407) on Hebrews 9:28. “So Christ was once offered.”: By whom offered? evidently by Himself. Here he says that He is not Priest only, but Victim also, and what is sacrificed. On this account are [the words] “was offered.” “Was once offered” (he says) “to bear the sins of many.” Why “of many,” and not “of all”? Because not all believed, For He died indeed for all, that is His part: for that death was a counterbalance against the destruction of all men. But He did not bear the sins of all men, because they were not willing. And what is [the meaning of] “He bare the sins”? Just as in the Oblation we bear up our sins and say, “Whether we have sinned voluntarily or involuntarily, do Thou forgive,” that is, we make mention of them first, and then ask for their forgiveness. So also was it done here. Where has Christ done this? Hear Himself saying, “And for their sakes I sanctify Myself.” (John 17:19) Lo! He bore the sins. He took them from men, and bore them to the Father; not that He might determine anything against them [mankind], but that He might forgive them. NPNF1: Vol. XIV, Epistle to the Hebrews, Homily 17. Elsewhere, he does affirm what we would understand to be a penal substitutionary atonement... Chrysostom (349-407): In reality, the people were subject to another curse, which says, “Cursed is every one that continueth not in the things that are written in the book of the Law.” (Deuteronomy 27:26.) To this curse, I say, people were subject, for no man had continued in, or was a keeper of, the whole Law; but Christ exchanged this curse for the other, “Cursed is every one that hangeth on a tree.” As then both he who hanged on a tree, and he who transgresses the Law, is cursed, and as it was necessary for him who is about to relieve from a curse himself to be free from it, but to receive another instead of it, therefore Christ took upon Him such another, and thereby relieved us from the curse. It was like an innocent man’s undertaking to die for another sentenced to death, and so rescuing him from punishment. For Christ took upon Him not the curse of transgression, but the other curse, in order to remove that of others. For, “He had done no violence neither was any deceit in His mouth.” (Isaiah 53:9; 1 Peter 2:22.) And as by dying He rescued from death those who were dying, so by taking upon Himself the curse, He delivered them from it. NPNF1: Vol. XIII, Commentary on Galatians, Chapter 3, v. 13. Greek text: Καὶ μὴν ἑτέρᾳ κατάρᾳ ὁ λαὸς ὑπεύθυνος ἦν τῇ λεγούσῃ· Ἐπικατάρατος πᾶς, ὃς οὐκ ἐμμένει ἐν τοῖς γεγραμμένοις ἐν τῷ βιβλίῳ τοῦ νόμου. Καὶ τί τοῦτο; Ὁ μὲν γὰρ λαὸς ὑπεύθυνος ἦν· οὐ γὰρ ἐνέμεινεν, οὐδὲ ἦν τις ὁ πεπληρωκὼς τὸν νόμον ἅπαντα. Ὁ δὲ Χριστὸς ἑτέραν κατάραν ταύτης ἠλλάξατο τὴν λέγουσαν· Ἐπικατάρατος πᾶς ὁ κρεμάμενος ἐπὶ ξύλου. Ἐπεὶ οὖν καὶ ὁ κρεμάμενος ἐπὶ ξύλου ἐπικατάρατος, καὶ ὁ τὸν νόμον παραβαίνων ἐπικατάρατος, μέλλοντα δὲ ἐκείνην λύειν 61.653 τὴν κατάραν ὑπεύθυνον οὐκ ἔδει γενέσθαι αὐτῆς, δεῖ δὲ δέξασθαι κατάραν ἀντ' ἐκείνης, τοιαύτην ἐδέξατο, καὶ δι' αὐτῆς ἐκείνην ἔλυσε. Καὶ καθάπερ τινὸς καταδικασθέντος ἀποθανεῖν, ἕτερος ἀνεύθυνος ἑλόμενος θανεῖν ὑπὲρ ἐκείνου, ἐξαρπάζει τῆς τιμωρίας αὐτόν· οὕτω καὶ ὁ Χριστὸς ἐποίησεν. Ἐπειδὴ γὰρ οὐχ ὑπέκειτο κατάρᾳ τῇ τῆς παραβάσεως, ἀνεδέξατο ὁ Χριστὸς ἀντʼ ἐκείνης ταύτην, ἵνα λύσῃ τὴν ἐκείνων· Ἁμαρτίαν γὰρ οὐκ ἐποίησεν, οὐδὲ δόλος εὑρέθη ἐν τῷ στόματι αὐτοῦ. In Epistolam Ad Galatas Commentarius, Caput III, v. 13, PG 61:652-653.