For Moses writes about the righteousness that is based on the law, that the person who does the commandments shall live by them. (ESV)
As you read this verse you should be so thankful that you are made right with God by grace and not by works of the Law. Paul is reminding his readers that the righteousness that is based on the Law required complete and total obedience to every commandment. Moses, who wrote down the Law of God, could not keep the holy requirements of the Law himself!
If you talk to the average sinner on the street they will give you some sort of reason why they are "righteous." They will likely say that they have never killed anyone. They try to not to do harm to their neighbor. They are not as bad as someone else like Hitler, Stalin, Mao, or some other monster. They are appealing to righteousness based on law; in this case, their own law.
The average person on the street, if pressed further, will have to admit that they do not even keep their own law, much less God's. The reality is that we are all wretched sinners. The Law of God serves to point out that we are all rebels to the Law of God. Those who want to keep it are unable to because of our flawed and broken nature. There is a reason why it is often called depraved nature.
The first step in receiving the true righteousness of God is an honest admission of our own guilt. Jesus, who came to provide for our righteousness, pointed out that those who thought they were keeping the letter of the law failed in keeping the heart of it. Remember, he said that those who said they did not murder, had also said they hated their brother. He said, hate is the same as the act of murder.
What's the point? We are all sinners. From Moses to you and I we are incapable of keeping the Law. I encourage you to confess your sin, receive God's offer of free forgiveness purchased by the sacrifice of Jesus Christ, and you will receive righteousness as a gift, not based on your own futile works.