I last read the book in the early 90's, so it would have been written before then.
The main plot is about an Earth person being sent on an undercover mission to an alien planet of extraordinarily handsome/beautiful people who resemble humans in every detail but one- the cartilage in their nose. These aliens are either trying to avoid contact with humans, or invade (I can't remember which), but their leader is not 100% decided.
Their leader is appointed by being the best player on their world of a game very similar to chess. The human agent is a grand master of chess, and is sent there undercover, to play and win the title of leader, so that he can facilitate contact or avoid the forthcoming war.