From Zobrist 2000: 367:

[S]ince all possible chess games can be expressed in a tree ..., it is known that there is a perfect strategy for chess that guarantees a win or a draw for one player. Of course, the strategy has never been found. It is the combinatorics of game playing that prevent the discovery of perfect strategies. In chess, when it is a player's turn to move, that player has, on the average, 30 legal moves resulting in 30 different positions. If the opponent also has 30 replies to each of those moves, then 900 positions result. This sort of calculation gives an estimate of 10^125 as the size of the lookahead tree for chess (the number of paths from the top of the tree to the terminal positions). If a computer could examine a billion positions per second, it would still take 10^108 years to examine the entire lookahead tree to determine the optimal strategy. It should be mentioned that the number of board positions is far smaller, approximately 10^42, so it is theoretically possible to store all positions together with their optimal moves in a large table. Storing one board position on an element the size of an atom would necessitate a memory of about the size of the earth.