Create a grid in Illustrator

I have a map that is made up of squares. I need the horizontal lines and vertical lines of the grid to match up with the edges of the squares on the map as if you filled the intersecting lines with dark blue. It's an easy job just takes a little bit of time. If you see the attached file you can tell how the lines do not match up with the edges of the squares. I have the AI file in CS6.