I can deal with roundabouts; it's the other idiots that can't seem to figure out how to properly yield that make them unpleasant for me. I have to pray that I don't get cut off from when another car approaches when I'm already in the roundabout.
Remember, if you feel that way about others, others are probably thinking the same thing about you as you approach a roundabout!
Ah, I see the warning signs now.
Technically, warning signs don't tell you what to do, just what to watch out for. I'm struggling to come up with any guidance in the Illinois Vehicle Code on what to do at a roundabout or traffic circle, so it's possible it's actually a legal loophole.
I would think basic intersection protocal would apply (ie: keep right).
Or, to think about it this way: If you turned left in front of the island, and another car hit you head on, would you think the car on the right (the one you hit) have the right of way, or would you (on the left) have the right of way? That seemingly makes the answer much clearer.