I would use 5 min epoxy. Be sure to wipe off excess w/alcohol, make sure piece stays aligned and hold in place til set. If you use a slower setting glue, you can tape the piece in place...just make sure it doesn't shift out of alignment.
Luckily you have the chip that came off. It should be a simple and quick fix. If you use Titebond II or III waterproof glue its a easy clean up with water. Coat both surfaces with a small paint brush, place the piece in position and add some tape to keep it in place. After it sets up you can carefully buff the area with a small piece of 220 grit to further clean up any left over evidence of the repair.
Mike's info is the best and easiest. Epoxy is good as well. If you use epoxy don't simply wipe off any squeeze out. It will spreed around and change the look of the cork in the area. Clean up any squeeze out with distilled vinegar.