Let me briefly describe the method.
A chess board consists of an 8x8 array displaying two different alternating shades of wood. Therefore we'll need nine  "with the grain" strips, four of one shade, five of the other. You'll need an extra square that will eventually get cut off. [Update: Please no comments on the use of 8 or 9 strips, this was the method I used.] The strips are laid down in alternating shades. Glued. Then stripped at 1 3/4" "cross grain". The new strips, with alternating 1 3/4" squares, are then shifted to oppose the shade beside them. Glued. And then the extra is trimmed off.
Visualize it or practice with paper.
Above is the results of the first cuts.