[Faramir Jones]

I have a theory that the two chests Bilbo took with him on his return journey from the Lonely Mountain are payment for two services rendered by him to the dwarves, not covered by the original contract: his rescuing them from the spiders; and secondly, his rescuing them from the Elvenking's cells.

I suggest this because, when the Mountain’s secret entrance was found, Thorin pointed out that now was Bilbo’s time ‘to perform the service for which he was included in our Company’, the time for him ‘to earn his Reward.’ Bilbo was a little indignant, because

I have got you out of two messes [the spiders and the Elvenking’s cells] already, which were hardly in the original bargain, so that I am, I think, already owed some reward. (My italics)

One could argue that Bilbo has already taken and disposed of his fourteenth share, in the shape of the Arkenstone; but that he still felt he was owed something for dealing with the 'two messes'.