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Short answer is no. One estimate says there are 10^120th possible chess games. I'm not doing the math now, but I believe that falls into the not-physically possible within our lifetime using known physics. An "If you had started calculating at the beginning of the universe, you wouldn't have even tackled a sliver of the work by now" type of problems.

http://www.popsci.com/science/article/2010-12/fyi-how-many-d...

What I mean by solving "every" move is that the AI would be able to determine which trees are a "losing" state and not continue, removing well over 99% (or 99.999% I don't know) of the possible games. I guess maybe solve is not the correct answer but something like 99% presumption on the best or best 3 moves.

AlphaGo's strength is in choosing which moves to consider. Solving a game means considering every move (up to alpha-beta pruning) -- AlphaGo's techniques don't help with this.

There are effectively limitless possibilities in terms of playouts of chess

no