What does Bilbo give to Frodo as a gift which later saves him from being killed by a troll?

Bilbo gives Frodo a mithril vest, also called a mithril shirt or coat, which later protects him from a cave troll’s spear in Moria. The weapon strikes Frodo in the chest but cannot penetrate the exceptionally strong metal.

Bilbo originally received the garment from Thorin Oakenshield during the events of The Hobbit. It was made from mithril, a rare, lightweight, silver-colored metal prized by the Dwarves. In The Lord of the Rings, Bilbo passes it to Frodo before Frodo leaves Rivendell with the Fellowship.

The scene is a key example of Tolkien’s setup and payoff: an apparently extravagant gift becomes essential protection later in the story. The vest does not make Frodo invulnerable; it protects against the troll’s thrust, while he remains vulnerable to other weapons and dangers. “Sting” was another weapon Bilbo gave Frodo, but it is not the gift that saves him from the troll.