"For all who rely on works of the law are under a curse; for it is written, 'Cursed be everyone who does not abide by all things written in the Book of the Law, and do them.' Now it is evident that no one is justified before God by the law, for 'The righteous shall live by faith.'"
- Galatians 3:10-11
In verse 10 Paul refers to what is traditionally entitled the Covenant of Works. The Westminster Confession of Faith (VII:2) explains this: "The first covenant made with man was a covenant of works, wherein life was promised to Adam, and in him to his posterity, upon condition of perfect and personal obedience." Adam was promised eternal life after perfectly fulfilling all the commands of his Creator, in nature, intent, and action. In his created state, Adam was capable of this state of holiness, would have been confirmed in that state, and his posterity would have inherited that native holiness.
However, as every child in Sunday school has learned, Adam broke the covenant, disobeying God in eating from the forbidden tree. He provoked the wrath of God, and forever forfeited the eternal life promised in that covenant, for himself and his posterity.
However, while justice would surely have allowed God to take no further concern with His rebellious children, in His love and grace He chose to establish a second covenant, the Covenant of Grace. As the Confession continues (VII:3), "Man by his fall having made himself incapable of life by that covenant [i.e., of works], the Lord was pleased to make a second, commonly called the Covenant of Grace; wherein He freely offereth unto sinners life and salvation by Jesus Christ, requiring of them faith in Him that they may be saved, and promising to give unto all those that are ordained unto life, His Holy Spirit, to make them willing, and able to believe." Or in Paul's words (Rom. 1:17, Gal. 3:11, from Habakkuk 2:4), "The righteous shall live by faith."
If you look to your works to justify you before God, then you are relying on a Covenant that will now save no man, because its standard is perfection, in nature, intent, and action. For us, the fallen descendants of Adam, there is only one hope, and that is faith in the works and person of our Redeemer, Jesus Christ.