The Holy Bible, Revelation 20:1-3

1 And I saw an angel come down from heaven, having the key of the bottomless pit and a great chain in his hand.

2 And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years,

3 And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled: and after that he must be loosed a little season.

The Book of Mormon, 1 Nephi 22:26

26 And because of the righteousness of his people, Satan has no power; wherefore, he cannot be loosed for the space of many years; for he hath no power over the hearts of the people, for they dwell in righteousness, and the Holy One of Israel reigneth.

The Doctrine and Covenants, Section 101:28

28 And in that day Satan shall not have power to tempt any man.

The Doctrine and Covenants, Section 45:55

55 And Satan shall be bound, that he shall have no place in the hearts of the children of men.

The Doctrine and Covenants, Section 88:110

110 And so on, until the seventh angel shall sound his trump; and he shall stand forth upon the land and upon the sea, and swear in the name of him who sitteth upon the throne, that there shall be time no longer; and Satan shall be bound, that old serpent, who is called the devil, and shall not be loosed for the space of a thousand years.

Doctrine and Covenants Student Manual, Section 43

There are many among us who teach that the binding of Satan will be merely the binding which those dwelling on the earth will place upon him by their refusal to hear his enticings. This is not so. He will not have the privilege during that period of time to tempt any man.—Quote by Joseph F. Smith (D&C 101:28.)

History of the Church, Joseph Smith 4:576

It would seem also, that wicked spirits have their bounds, limits, and laws by which they are governed or controlled, and know their future destiny; hence, those that were in the maniac said to our Savior, “Art thou come to torment us before the time,” and when Satan presented himself before the Lord, among the sons of God, he said that he came “from going to and fro in the earth, and from wandering up and down in it;” and he is emphatically called the prince of the power of the air; and, it is very evident that they possess a power that none but those who have the Priesthood can control, as we have before adverted to, in the case of the sons of Sceva.

Journal of Discourses, Orson Pratt 16:42

The question may arise here–”Will it be possible for men to sin during the Millennium?” Yes. Why? Because they have not lost their agency. Agency always continues wherever intelligent beings are, whether in heaven, on the earth, or among any of the creations that God has made; wherever you find intelligent beings, there you will find an agency, not to the same extent perhaps, under all circumstances, but yet there is always the exercise of agency where there is intelligence. For instance, when Satan is bound and a seal set upon him in this lowermost pit, his agency is partially destroyed in some things. He will not have power to come out of that pit; now he has that power; then he will not have power to tempt the children of men, now he has that power; consequently his agency then will be measurably destroyed or taken away, but not in full. The Lord will not destroy the agency of the people during the Millennium, therefore there will be a possibility of their sinning during that time. But if they who live then do sin it will not be because of the power of the devil to tempt them, for he will have no power over them, and they will sin merely because they choose to do so of their own free will.