Bilbo found the Arkenstone in Smaug's treasure chamber.
Bilbo gave the Arkenstone to Bard so he could use it to stop a battle between the Elves, Men, and Dwarves. It did not work.
He brings the Arkenstone to Bard to pay off the 1/13 of the share of treasure. Thorin reacts in anger when he finds out that Bilbo gave Thorin's family treasure to Bard.
It was in Smaug's hoard in the Lonely Mountain. When Bilbo went down there he saw it, took it, and kept it a secret from everyone else.
He retrieves it when he is escaping Smaug
Bilbo takes possession of the Arkenstone without telling Thorin.
Bilbo took the Arkenstone. It was the treasure Thorin desired most.
Bilbo claimed that under the terms of the contract he was due a proportion of the dragon's treasure, and that he had taken the Arkenstone as his share.
Bilbo Baggins gave the elvenking the Arkenstone, the prized possession of Thorin.
Bilbo takes the Arkenstone. He isn't entirely sure why he does it, but he picks it up and knew exactly what it was. He had some idea it might be of use later on.
Biblo 'borrows' the Arkenstone.
Bilbo takes possession of the Arkenstone without telling Thorin.
Bilbo took the Arkenstone. It was the treasure Thorin desired most.
The Arkenstone of Thrain.
Bilbo claimed that under the terms of the contract he was due a proportion of the dragon's treasure, and that he had taken the Arkenstone as his share.
The Arkenstone
He had possession of the Arkenstone.
Bilbo Baggins gave the elvenking the Arkenstone, the prized possession of Thorin.
Bilbo took the Arkenstone from Smaug's treasure trove. He gave it to the men to use as a negotiating tool.
Bilbo takes the Arkenstone. He isn't entirely sure why he does it, but he picks it up and knew exactly what it was. He had some idea it might be of use later on.
Bilbo hides the Arkenstone from the dwarves because he knew each one was greedy for the Arkenstone and they might kill each other or harm others for it.
Smaug has the Arkenstone in his hoard. Bilbo acquires it from the pile of treasure. He then gives it to Bard. Bard puts it with Thorin when he is buried. That is where it stayed.