In re the post below, Will reminds me that while chess may never be solved, it may still be theoretically possible to solve it. Of course he's right about the distinction between solvable and solved, but I'm still not convinced it's even possible to solve chess. Will suggests that because there is a finite number of possible chess games, there must be a solution (and this position is elaborated in a comment below).
But what would that solution look like? To me, a solution means a series of axioms that define best play, and while the list could be long and complex, I'm not comfortable with calling the exhaustive elaboration of all possible games a solution. Isn't a solution supposed to simplify matters? The solution to tic-tac-toe can be explained without actually showing every possible outcome.
I have a feeling "solution" isn't even a meaningful term for experts on systems as complex as chess; they're probably more concerned with completeness or some other technical measure of freedom. After all, moves in chess aren't usually forcing, which means there vast periods during which a player can direct her own strategy and take the game in radically different directions depending on what that strategy is. Can you imagine someone just sitting down for a game of chess, proclaiming, "Mate in 39!" without making a single move? This will never happen, because the players in chess have too many degrees of freedom.