18 Then after three years, I went up to Jerusalem to get acquainted with Cephas and stayed with him fifteen days. 19 I saw none of the other apostles—only James, the Lord's brother. 20 I assure you before God that what I am writing you is no lie.
21 Then I went to Syria and Cilicia. 22 I was personally unknown to the churches of Judea that are in Christ. 23 They only heard the report: "The man who formerly persecuted us is now preaching the faith he once tried to destroy." 24 And they praised God because of me. (TNIV)
In this section Paul continues along in his defense of himself and his gospel. As McKnight notices, this portion of chapter one has essentially the same argument as 1:13-17, it just concerns a different or perhaps more specific set of authorities. Within three years of his call, Paul went up to Jerusalem to meet Peter. The emphasis here is the shortness of his stay with Peter. His reference to being with Peter for 15 days is sandwiched between a reference to three years of ministry prior in 1:18 and 14 years following in 2:1. Paul had already been active prior to meeting Peter and his stay certainly wasn't long enough to have learned his entire gospel there. Paul is stressing that neither Peter, James, nor anyone at Jerusalem was in authority over him or had commissioned him. Certainly Paul and Peter discussed Jesus, and Peter may have even filled Paul in on aspects of the Jesus tradition that he was ignorant of, but Peter was not the source of Paul's gospel.
In verse 20 Paul takes an oath. This reveals two things. First, what he was saying was contested. Other people were saying things that disagreed with the way Paul told his story, otherwise the oath would be unnecessary. Second, taking an oath was serious. Paul's reputation hinged on the truthfulness of what he said. It shows that we need to slow down and really absorb the argument in this part of the letter or we will miss something important.
Paul continues to tell us about his past in the following paragraph. He doesn't go into many details about his time in Cicilia and Syria because his main focus is still his relationship to the Jerusalem church. He was unknown there, and thus clearly not under their jurisdiction.
As Hays points out, not only is Paul silent about control from Jerusalem, but there also seems to be approval coming from them. His meeting with Peter goes off without a hitch and the church in Jerusalem praised God at his conversion and preaching. There seems to be general agreement between the Jerusalem church and Paul. Hence, if a segment of the Jerusalem church is now opposing Paul, it's an about-face on their part not his. Paul's gospel is the constant (as he notes in 1:6-8).
One phrase that we can't overlook is 'in Christ' in verse 21. It's easy to pass over it as a throw away phrase but it's highly significant. In this context it is somewhat polemical. The Jerusalem church was accepting of his gospel, the gospel of Christ through which we become in Christ. Being in Christ is the foundation of Christian fellowship, not adherence to the Law as the Teachers incorrectly claimed.