Bilbo's Mithril Shirt was a shirt of chain mail, alternately described as a vest and a coat, made from mithril. It has moved several times during the course of the series, from Smaug's hoard to Bilbo to the Mathom-House to Frodo. It was taken by the Orcs of Cirith Ungol from Frodo, but was later with the Mouth of Sauron, as he showed it to Gandalf, Aragorn, and the other leaders outside the Morannon in the Battle of the Black Gate. And he died.
The origins of the shirt are unknown, but it came to be part of the Dwarven treasure hoard of the Lonely Mountain. It was found by the dragon Smaug and added to his treasure heap. Here, it was given by Thorin II Oakenshield to the Hobbit Bilbo Baggins, who wore it during the Battle of Five Armies. After returning to the Shire, Bilbo donated the shirt to the Mathom-house. Before departing The Shire for Rivendell, Bilbo the shirt and wore it on that journey.
Many years later it was gifted by Bilbo to his nephew Frodo Baggins as Frodo set out on his quest to Mount Doom to destroy the One Ring. Frodo hid the chain shirt under his tunic unknown to the rest of the Fellowship. It was discovered when, during a battle in the mines of Moria, an orc chieftain threw his spear at Frodo (Alternatively, in the Peter Jackson film it was a troll who speared Frodo). The shirt prevented what would have been a lethal wound, leaving Frodo severely bruised but still alive.
The shirt was taken from Frodo in the tower of Cirith Ungol. The two groups of orcs which captured Frodo fought over the valuable shirt, and most were killed during the conflict. One of the two orcish leaders, Shagrat, survived the fight and seized the shirt for himself, escaping the tower with it after Samwise Gamgee rescued Frodo. The shirt eventually ended up in the possession of the Mouth of Sauron at Barad-dûr, where he presented it to Gandalf at the Black Gates as false evidence that Frodo had failed in his quest. In his wrath Gandalf retrieved the shirt. The wizard later returned it to Frodo after the destruction of the Ring.