Use a screw extractor like a normal screwdriver to remove the screw. Be sure to go slowly, and press down hard enough to prevent slippage and engage the burrowing threads.
If the screw extractor can't get a grip, you may need to drill a small hole into the screw head. You will need a drill bit that is designed for drilling metal; a wood-drilling bit won't survive. Be careful! If you drill too far, you will destroy the head entirely or make it fragile enough that it will snap off, making it even harder to get the screw out.
Also try using a small piece of steelwool or a piece of the green abrasive on kitchen cleaning sponges- press a small piece into screw head, insert screwdriver and turn.
The abrasive material will bite into the screwhead, and give better grip for the screwdriver.
As a last resort if the screw is too badly damaged for the screw extractor to work properly you may have to drill out the hole using a bit size the same as the shaft of the screw. Remember to work incredibly slowly, use a tool to hold the piece in place and you can never be too paranoid when working with such small screws to make sure you're not going too far.