If you're using photoshop (these might work for others such as GIMP, though I've never used it before):
1. Make a new 200x200 image and fill the backround with black.
2. Make 2 100x100 white squares, one in the top left corner, other in the bottom right corner (they should meet at the center and create a simple 4 square checkerboard).
3. Save it as a pattern (Edit -> Define Pattern)
4. Fill your canvas using the patten, then just crop away (I select the whole thing, contract the selection, invert the selection, delete (this gets rid of some of the outside), invert again, contract a little more than delete the inside.

You can make you initial pattern bigger or smaller depending on how...checkery you want the border.

For the inner one I simply inverted the colors.