3:21 But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;

This is the righteousness that is a free gift from God.  It comes as we yield the members of our bodies to His Holy Spirit.  This is the purpose of grace, that we might work the works of God.  Our part is to submit.  God's part is to do His works through us.

1 John tells us not to be deceived.  It says that he who does righteousness is righteous.  This righteousness from God is real.  God does real works through us if we will only yield to Him.