The accepted answer is wrong, due to the fallacy of accepting a link to a another website as the truth, rather than actually doing the math.
Particularly, the site http://mathworld.wolfram.com/Chess.html confused the number of positions, with the number of 40-move games.
Though mathworld says
The number of possible games of 40 moves or less P(40) is approximately 10^(40) (Beeler et al. 1972)
The Beeler reference itself is very clear that it means positions, not games:
There are about 10^40 possible positions
and though mathworld says
Shannon (1950) gave the estimate ... 10^43
Shannon really wrote in XXII. Programming a Computer for Playing Chess Philosophical Magazine, Ser.7, Vol. 41, No. 314 - March 1950 :
In typical chess positions there will be of the order of 30 legal moves. The number holds fairly constant until the game is nearly finished as shown in fig.
- This graph was constructed from data given by De Groot, who averaged the number of legal moves in a large number of master games (De Groot, 1946, a). Thus a move for White and then one for Black gives about 1000 possibilities. A typical game lasts about 40 moves to resignation of one party. This is conservative for our calculation since the machine would calculate out to checkmate, not resignation. However, even at this figure there will be 10^120 variations to be calculated from the initial position.
...
Another (equally impractical) method is to have a "dictionary" of all possible positions of the chess pieces. For each possible position there is an entry giving the correct move (either calculated by the above process or supplied by a chess master.) At the machine's turn to move it merely looks up the position and makes the indicated move. The number of possible positions, of the general order of 64! / 32!(8!)^2(2!)^6, or roughly 10^43
In chess, "40 move game" means each player moves a piece 40 times: 80-ply or 80 half moves.
in standard chess terminology, one move consists of a turn by each player; therefore a ply in chess is a half-move. Thus, after 20 moves in a chess game, 40 plies have been completed—20 by white and 20 by black.
So for a 40 move game, if it is approximated that there is some constant (c) number of legal half-moves, the approximation of the number of 40 move games is of the form:
c ^ 80
So as long as "c" is greater than 10, the number of 40 move games is greater than the number of atoms in the universe.
For example, there are 20 possible first half-moves (16 pawn moves and 4 knight moves), and 20 possible second half moves.
So Shannon, citing to De Groot uses the estimate of "30" for "c" and therefore:
30^80 = ~1.5 x 10^118
So, yes, there are more exactly 40 move (80-half move) games than the number of atoms in the universe.