"You seek that which would bestow upon you the right to rule: the king’s jewel. The Arkenstone. It is precious to you beyond measure. I understand that. There’s gems in the mountain that I too desire. White gems of pure starlight.”

This was actually one of my favourite parts of The Hobbit, because it pretty much confirms that the Silmarils are in the mountain. Although I'm still a firm believer that the Arkenstone itself is the Simlaril that was lost under the earth.
(credit to thranduilings.tumblr.com for the gis)