[Mithadan]

Someone has studied law.

The precise terms offered were "cash on delivery, up to and not exceeding one fourteenth of total profits (if any)".

The modification of the contract, which as William comments" does not exclude the Arkenstone nor specifically include it, is found after Bilbo returns from his meeting with Smaug, and Thorin, who states "as to your share, Mr. Baggins, I assure you we are more than grateful and you shall choose your own fourteenth, as soon as we have anything to divide."

So if this modification was valid, Bilbo certainly had the right to select the Arkenstone as part of his share. From his perspective, he had not broken any covenant and had chosen some of his share. I am not troubled by this as any breach of faith.

Now let's play at law (cannot resist). One could question whether, at the time he took the stone, there was anything to divide yet, since Smaug's death was not known. One could also debate the enforceability of the modification which was not supported clearly by consideration (Bilbo had not done anything or agreed to do anything he had not already agreed to do, so Thorin did not receive anything in exchange for the promise). Peppercorns anyone?