Let us try a quick back-of-envelope estimation:

The number of chess games possible might be around 50 moves a side times 20 options per move, making 20^100 different games.

The number of atoms in the observable universe might be around 10^25 per kilogram times 2 * 10^30 kg per solar system times 10^14 stars per galaxy times 10^14 galaxies in the observable universe.

Comparing the very large numbers, 10^83 is clearly less than 20^100, so the conjecture is probably true.