Our righteousness rests alone on Christ the Lord. Our righteousness rests on Christ's entire person, who as God and man is our Righteousness in His complete obedience.
Even if Christ had been conceived and born without sin by the Holy Spirit and had fulfilled all righteousness in His human nature alone, and yet had not been true and eternal God, this obedience and suffering of His human nature could not be credited to us for righteousness. Also, if God's Son had not become man, the divine nature alone could not be our righteousness. We believe, teach, and confess that the entire obedience of Christ's entire person (which He has offered to the Father for us, even to His most humiliating death on the cross) is credited to us for righteousness.
The obedience not only of one nature, but of the entire person, is a complete satisfaction and atonement for the human race. By this obedience God's eternal righteousness, revealed in the Law, has been satisfied. Our righteousness benefits us before God and is revealed in the Gospel. Faith relies on this before God, which God credits to faith, as it is written in Romans 5:19:
For as by the one man's disobedience / the many were made sinners,
so by the one man's obedience / the many will be made righteous. (paragraphs 55-57)
Condensed from CONCORDIA: THE LUTHERAN CONFESSIONS, copyright 2005,2006 by Concordia Publishing House. Used by permission. All rights reserved. To purchase a copy of CONCORDIA, call 800-325-3040.