"Faith spans the gap between the present and the day of judgment. It is the true worship, which sets the believer in constant movement forwards, and which counts as righteousness before God (Phil. 3 verses 3, 9). Paul has it as his aim 'that I might be found in him not having my own righteousness which is from the law, but the righteousness which through "the faith of Christ", the righteousness from God on the basis of faith' (verse 9). Here he has in view the day when God will examine him, and hopes to meet that judgment with the 'righteousness of faith'. The righteousness Paul desires come from God, 'on the basis of faith'. Faith, not the righteousness from the law, constitutes piety before God. Yet this righteousness accorded to faith is an 'alien righteousness', which does not belong to Paul as his righteousness from the law once did. Faith and its righteousness from the law once did. Faith and its righteousness are present only "in Christ'. The 'faith of Christ' is faith which has its source in him, in his death and resurrection (verse 9). Paul's thought here is very close to his discussion of Abraham's faith in Romans 4. The 'righteousness from God on the basis faith' is at once absolute gift and recompense of obedience. "
- from Mark Seifrid's book "Christ, our Righteousness" pg. 90