A checker board is basically 64 squares (8 rows and 8 columns) with alternating red and black color. We could create a small rectangle and duplicate it over and over again until we have the checker board filled out, but that would take forever. This tutorial will show you a much easier way!
Step 1
Using the Rectangle Tool, draw out a rectangle, the size you'd like your checker board to be. Make the fill color red and the stroke black.
Step 2
Go to Object > Path > Split Into Grid. You'll get the following screen. Make sure to create 8 rows and 8 columns and set the gutter to 0.
You should get the following result:
Step 3
All that's left now is to add the black squares! Each square is it's own path. So you can select each square and change its color. You could hold Shift down when selecting each alternate square and then click on the black swatch. This will apply a black fill to the squares you selected. Another method is if you have Black as the fill color already, choose your Eye Dropper Tool and while holding down Alt click on the squares you want to turn black.
Here's my final result. King Me!
Here's another design I created using the Grid method:
More Vector Graphics: 
