Mathematically, chess has been solved by the Minimax algorithm, which goes back to the 1920s (either found by Borel or von Neumann). Thus, a turing machine can indeed play perfect chess.
However, the computational complexity of chess makes it practically infeasible. Current engines use several improvements and heuristics. Top engines today have surpassed the best humans in terms of playing strength, but because of the heuristics that they are using, they might not play perfect when given infinite time (e.g., hash collisions could lead to incorrect results).
The closest that we currently have in terms of perfect play are endgame tablebases. The typical technique to generate them is called retrograde analysis. Currently, all position with up to six pieces have been solved.
