I just spotted today that chess is now available on the US Amazon Kindle Store. The product details indicate that it was released on 9 February 2011.
Might this be an indication that Kindle apps and games might be coming the UK Amazon Kindle Store sometime soon? I do hope so.
Update
21 January 2015
I’ve just come across this post about four years later. I never did get a game of chess on my Kindle before I sold it. 🙁