More than 64.
We would need to know whether there is a border around the playing squares or if they go to the very edge of the board.
Regardless, i'm too lazy to Google it or count, but it's something like 120. [Edit, after reading posts 5 & 6 and taking another sip of Scotch:] ...give or take 84ish.
Or not.
This is a trick question. Lets see if any of you can figure it out.