Broken bolt

[tsubaki]

I've not bought them yet but there are reverse drill bits available. Basically it drills in reverse helping in a situation like this.
Start spraying with a real good penetrating oil. The best one I've found is made by Mopar.
Drill the hole best as you can in the center, if you get lucky and stay centered and drill to the end of the bolt you can scoot more penetrating oil to the rear. Then use an extractor and hope for the best.
If all else fails, you will have to Heli-coil it.