For Paul in Galatians 3, baptism and faith are so closely related as effectively to be synonyms for one another, to be used synonymously in parallel arguments. This is a particularly significant fact, one with important consequences for our understanding of the proper relation between faith and religious actions, as well as for our interpretation of Paul's understanding of salvation.
Consider the argument of the first nine verses of the chapter. There Paul asks the question: Did you receive the Spirit by doing works of the law or by believing what you heard? (3.2). It is clear that by doing this, he is setting up faith and works of the law as alternative means to accomplishing the same end, namely the reception of the Holy Spirit. If the object is obtained by one means, it would make no sense to take up the other means; that is Paul's argument. Having started with the Spirit, are you now ending with the flesh? (v. 3).
He goes on to make the connection between the reception of the Holy Spirit, on the one hand, and the blessing of Abraham and his offspring, on the other. The promise in the scripture -- "All the Gentiles shall be blessed in you" -- quoted in v. 8 is applied to the case of the believing Galatians who have the Spirit of God: For this reason, those who believe are blessed with Abraham who believed (v. 9).
Even further, he later speaks explicitly of the promise of Abraham as the reception of the Holy Spirit. Christ becomes a curse to redeem those who were under the curse of the law, in order that in Christ Jesus the blessing of Abraham might come to the Gentiles, so that we might receive the promise of the Spirit through faith (v. 14). "Justification" by faith, the reception of the Holy Spirit, believing, receiving the promised blessing of Abraham -- all of these things are closely and intimately connected.
But now there is a complication introduced, namely the locution "in Christ." What does it mean to be in Christ? How can the promised Holy Spirit be received in Christ?
It becomes clear that Paul makes use of a concept of union with Christ. He explicitly names Christ as the singular offspring of Abraham in v. 16, the implication being that he has inherited the promised blessing of Abraham. This is certainly true: Christ received the Holy Spirit, just as Peter affirms in his sermon on Pentecost (Acts 2.33). Consequently if we are to have this blessing ourselves, we must be united to Christ in some relevant way.
We have already seen that Paul envisions faith as a condition of union with Christ, since it is through faith that one is justified, receives the Holy Spirit, is blessed alongside Abraham, etc. Yet he also speaks of baptism in the same way. Notice what he says:
Now before faith came, we were imprisoned and guarded under the law until faith would be revealed. Therefore the law was our disciplinarian until Christ came, so that we might be justified by faith. But now that faith has come, we are no longer subject to a disciplinarian, for in Christ Jesus you are all children of God through faith. As many of you as were baptized into Christ have clothed yourself with Christ. . . . And if you belong to Christ, then you are Abraham's offspring, heirs according to the promise (vv. 23-7, 29).
Notice that faith and baptism here are used in parallelism: to be in Christ by faith is to have been baptized into Christ; to belong to Christ and to be Abraham's offspring is to have clothed oneself with Christ through baptism.
Why is this important? There is at least one thing important about this: faith and religious action are so closely connected for Paul that he expects the person who has the one to have the other, as well. It would be inconceivable for Paul for someone to have faith and yet not to have been baptized. "In that case," he might say, "what is it that you believe, since the message is 'Repent and be baptized'?" The separation between faith and religious action is lamentable and disastrous, a misunderstanding of Paul altogether. He certainly speaks against keeping the Law, but evidently he expected that all believers would be baptized.