Still under siege inside the mountain, Thorin searches for the Arkenstone but Bilbo isn't telling that he has it. Thorin's dwarf kin is now but 2 days away from the mountain with an army of 500.
Tired of this whole business, Bilbo sneaks out of the mountain and seeks an audience with Bard and the elvish king at which time he offers them the arkenstone, telling them that Thorin values it above all else, even a river of gold. He then heads back to the dwarves.
Gandalf stops him on his return and praises his actions but says there is trouble brewing that no one else is aware of. Bilbo makes it back into the mountain unseen and goes to sleep (to dream of eggs and bacon). I GET IT ALREADY! HOBBITS AND DWARVES LIKE FOOD! Please, leave the food out of it now unless it actually has some relevance to the plot.
I somehow don't think Thorin is going to be happy about losing such a gem, not only in terms of it's value but it has sentimental value for him too. Me thinks poor Bilbo is in for a roasting when Thorin discovers his treachery.
Now, Thorin said he would talk terms but not until those outside laid down their arms and personally, I wouldn't talk to armed people either. Before you talk peace, it's normal to call a truce and not bring weapons to the negotiating table. Who responds to threats with acquiescence? Well, hobbits apparently.
I know this isn't exactly what I had in mind when I wrote my piece on chapter one, but my prediction has come true and one of the party had betrayed them. I think that makes Thorin Jesus rather than Bilbo.