In the film Edit
It is first used by Ditchwater Sal, which bound the lost princess Una through a trap to her and made her her slave. As Dunstan met Una he tried to free Una through cutting at the chain, but the silver thread just flipped together again. Una is only freed when Ditchwater Sal is killed by Lamia.
After having given birth to Tristan and sending the baby to Dunstan, she layed a piece of the magic chain in the basket, in which Tristan was found by Dunstan. Eighteen Years later Dunstan told Tristan about his mother and gives him three things: a babylon candle, a letter and a piece of the magic chain. Tristan later used the magic chain to bind Yvaine to him and also prevent her from running away as binding her at a tree.