Chess moves: how many are there?

Source: The Guardian

In Paul Hoffman's book King's Gambit: A Son, a Father and the World's Most Dangerous Game (published by Hyperion in New York in 2007), he states that: "In practice the possibilities in chess are boundless, although theoretically it is a mathematically finite activity – there are, for example, 988 million positions that can be reached after four moves for white and four for black." Can that figure possibly be correct? It seems far too big a number after so few moves for each side. And is the often quoted "fact" that there are more possible moves in a chess game than there are atoms in the universe really correct?

Find the discussions at - The Guardian - Notes & queries

One of the readers Mr. Ivanovich responds -

There are at least 100000000000000000000000000000000000000000 (10^39) times as many moves in chess as there are atoms in the universe.

The review of the book at The New York Times - 64 squares