Chess has 10¹²⁰ different positions. Checkers has only 10²⁰. Checkers has been solved. So no, I don't think chess will be solved ever as it has a googol times as many positions
No, chess has around 10^45 positions. You are thinking of the number of legal games.
This is still over 10^24 times as many as checkers, a game which took over 1000 years of computing time to solve.
My opinion is that chess, as a game played by humans, will never be "solved". As for a purely mathematical solution I have no idea but neither do I see it as a problem (or even an interesting question but then I´m no mathematician).