Here are some verses that cause me to believe this:
Romans 6:23 "For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord."
Ephesians 2:8-9 "For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; not as a result of works, so that no one may boast."
"6 For while we were still helpless, at the right time Christ died for the ungodly. 7 For one will hardly die for a righteous man; though perhaps for the good man someone would dare even to die. 8 But God demonstrates His own love toward us, in that while we were yet sinners, Christ died for us. 9 Much more then, having now been justified by His blood, we shall be saved from the wrath of God through Him. 10 For if while we were enemies we were reconciled to God through the death of His Son, much more, having been reconciled, we shall be saved by His life. 11 And not only this, but we also exult in God through our Lord Jesus Christ, through whom we have now received the reconciliation. 12 Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned - 13 for until the Law sin was in the world, but sin is not imputed when there is no law. 14 Nevertheless death reigned from Adam until Moses, even over those who had not sinned in the likeness of the offense of Adam, who is a type of Him who was to come. 15 But the free gift is not like the transgression. For if by the transgression of the one the many died, much more did the grace of God and the gift by the grace of the one Man, Jesus Christ, abound to the many. 16 The gift is not like that which came through the one who sinned; for on the one hand the judgment arose from one transgression resulting in condemnation, but on the other hand the free gift arose from many transgressions resulting in justification."
Romans 3:23-24 "