Two attempts to chain the wolf failed, and the third worked because it was not a chain. Gleipnir was made by dwarves out of six things that do not exist: the sound of a cat's footfall, the beard of a woman, the roots of a mountain, the sinews of a bear, the breath of a fish and the spittle of a bird. The list is an etymology in reverse, explaining why cats move silently and why women have no beards, and it is one of the neatest pieces of construction in the Norse material.
The wolf was not fooled. Suspecting a trick, he agreed to be bound only if one of the gods would place a hand in his mouth as a pledge of good faith, and Tyr did it knowing what would happen. When the fetter held, the hand was bitten off. Tyr is the god of the assembly and of sworn agreements, so the loss is the point: the gods secured the world by breaking their word, and the one who paid was the god of oaths.
At the end Fenrir breaks free, kills Odin, and is killed by Odin's son Vidar, who steps on the lower jaw with a shoe made from every scrap of leather ever discarded and tears the upper jaw away. The Gosforth Cross in Cumbria carries a figure prising open a beast's jaws, which is generally read as that scene, cut on a Christian monument in a region under Norse settlement.