The number of chess games is usually considered about 10 to the power 120, or sometimes it's more conservatively pruned down to 10 to the power 40 or so. Which is a mere trillion trillion thousand billion quadrillion billion.....(.... etc... etc....) To visualize this, if everyone on Earth paired off with another person to play a chess game every day, it would take trillions of years to finally play every possible chess game. Considering that the universe is a mere 14 billion years old, you can see just how large 10 to the power 40 is. In human terms it may as well be infinite. Yet the fact that Go is even more complex than this seems to some people to mean it's a deeper game!
In my opinion Chess and Go are the two best games yet invented, but I feel that some Go players get overly excited about game tree complexity.