Previously on Paul
... On the one hand, human faith does seem to be the major focus of what Paul has to say in places like Romans 4 and Galatians 3. When Paul says that "a person is justified [deemed right with God] by faith" (Rom. 3:28, NRSV), he is surely talking about our faith--the faith of Paul the Jew or Ken the Gentile. Paul does not seem to be talking about Jesus' faith here. He is laying down a general principle for how sinful people can be considered right with God, and the answer is "on the basis of [their] faith."
We see this line of thinking very clearly in Romans 4. "Blessed is the one against whom the Lord will not reckon sin," Paul says (4:8, NRSV). He is expanding on what it means for God to consider someone righteous (4:6) despite their sins (4:7) and ungodliness (4:5). His train of thought is clearly about the faith of sinful humans, not the faith of the sinless Jesus (cf. 2 Cor. 5:21).
Yet over time I have come to fall off the log also with those who think Paul, in both Romans and Galatians, started his argument by mentioning Jesus' faith, Jesus faithfulness and obedience to die on the cross. Both sides have made their cases, and neither side has a silver bullet. Where you end up is inevitably your sense of how all the little pieces add up and your overall sense of Paul's thinking in general.
For example, notice how redundant Paul's thought is in Galatians if he only has human faith in view:
Since a person is deemed right with God "through faith (pistis) in Jesus Messiah, we also have directed faith (pisteuo) toward Messiah Jesus, so that we might be deemed right by faith (pistis) in Messiah." 
Here's how I prefer to translate it:
Since a person is deemed right with God "through the faithfulness of Jesus Messiah, we also have directed faith toward Messiah Jesus, so that we might be deemed right through Messiah faith." 
Certainly Paul does not have to be concise, so this is no definitive argument that Paul had both Jesus' faith and our faith in view in this verse. It is just one point that eventually added up for me personally as a scholar.
But there are other arguments. For example, notice how similar Romans 5:19 is to this interpretation of Romans 3:22:
5:19: "through the obedience of the one man the many will be made righteous" (NIV).
3:22: "the righteousness of God through the faithfulness of Jesus to all who have faith." 
Clearly Paul had a place in his thinking for the obedient, faithful death of Jesus in us becoming right with God (cf. Phil. 2:6). But was he thinking this sort of thing in Romans 3:22? I will not go into further details in the main text here about what finally led me to see this as a "both/and" rather than an "either/or." 
You might wonder at this point what difference this whole debate makes, especially if everyone agrees that both the faithful death of Jesus and our faith in Jesus is important. True, beyond our desire in general to know accurately what Paul was really thinking, it is to a large extent a question of emphasis and tone. But I can think of three ways in which taking my interpretation points to three significant shifts...
 These two translations of Galatians 2:16 are mine.
 I prefer to leave the last faith expression ambiguous, "Messiah faith," in case Paul meant a double entendre here, a reference to both Christ's faith and our faith in Christ. Christ's faith is the basis for our justification, so we have put our faith in Christ. So in every way, it is "Christ-faith" that is the means of justification.
 My translation. Notice again how redundant this verse would be if human faith was only what Paul had in mind: "through faith (pistis) in Jesus to all who have faith (pisteuo)."
We can debate whether "righteousness of God" in 3:22 refers to God's righteousness or a righteousness he assigns to us. I tend to see a double entendre here of both, but in any case the idea that God deemes us righteous is obviously part of Paul's thought in the passage whatever the precise meaning of the phrase in this specific place.