Hmm, ok, so you want an idea that is completely original and not from anywhere on the internet, and you're asking someone on the internet to give you that answer? I don't think one is logically possible...
But a variation on an existing game is a possibility. You could have a look at variants of existing games and see if you can extend the range of variants in some way. For example look at all the chess variants http://www.chessvariants.com/
- this could give you some idea of new chess variants to come up with, or it could give you some idea on how to create a new variant of a different game, for example Backwards Chess is a well known variation http://www.chessvariants.org/index/m...backwardsstale
and maybe you could create a backwards version of something else: backwards draughts for example (not that one of course now, because that would be one you found on the internet, i.e. here).
If the long term aim of the project is to create such a game, you wouldn't necessarily have to create an AI for the game you come up with but you may be able to create a program that enforces the rules for a two player game (for example if a player tried to perform pawn e6-e4 in backwards chess, that would be impossible and would cause an error). But beware of thinking up a game with complex rules because you may be required in the next step to implement at least a rudimentary AI, and chess is a very difficult game to implement (I've tried! and even just to get all the moves sorted out for an exhaustive search chess puzzle solver takes a lot of work).