If you've got two light colors and two darks then you could do a strip set that alternates a light and a dark, light and dark, then slice them up into one inch segments, turn half so dark is at top and stitch those to the ones with light at top. If you want it to read clearly as a checkerboard then you will want to make sure that your lights are a similar value and intensity to each other and your darks are similar value and intensity to each other. That's still going to require a lot of matching up of intersections with small pieces.
Have you you looked into the stabilizers that have a grid on them? My understanding is that you fuse your squares to the grid, then going row by row flip right sides together sewing with 1/4" seam allowance. After sewing all rows, you then do same with columns. I'm trying to remember where I saw this, maybe in one of Joan Ford's books.
Rob