Rom 3:21-31, Rom 4-5.  All of the foregoing has been foundational to his main point:

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           BUT NOW a righteousness from God, apart from law, has been made known, to which the Law and the Prophets testify.  This righteousness from God comes through faith in Jesus Christ to all who believe (Rom 3:21-22).

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          The first three chapters or Romans were devoted to proving that all men are under the power of sin, and that the Law is insufficient to deliver them.  Now he makes a transition: "but now."  It is a new thing, a new act of God, a new dispensation equivalent to the handing down of the Law on Mt Sinai -- but, he quickly adds, the Old Covenant bears witness to its successor.

          

At the same time, this new righteousness abolishes the distinction between Jew and Gentile in the attainment of salvation:
 
           There is no difference,  for all have sinned and fall short of the glory of God, and are justified freely by his grace through the redemption that came by Christ Jesus (Rom 3:22-24).

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           This is stated more explicitly later on:

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           For there is no difference between Jew and Gentile—the same Lord is Lord of all and richly blesses all who call on him (Rom 10:12).

          

This is the kind of teaching that got him in trouble with the Hellenistic Jews. The claim that Jesus was the Messiah was not the thing that enraged them.  But that Jesus introduced a new mode of spirituality, one that supplanted the Temple and the Law, and that was open to Gentiles, was intolerable.   It was extremely important to these Jews to maintain the lines of distinction between themselves and the pagan Greeks.  And Paul attacked them on this very point -- in terms of righteousness, Jews were no better off than pagans.  He was overturning 1800 years of history and revelation!