In the wake of the release of the Chicago police shooting video, State Representative La Shawn Ford has proposed a bill allowing for the recall of the Chicago Mayor. The law would go into effect immediately, presumably allowing for the recall of Rahm Emanuel. It seems once again that Illinois likes to take an individual approach to recalls, rather than allow it for each official in the state.
The bill apparently would require 15% of turnout (in this case 86,000 valids) and at least 50 from each ward. The coverage I've seen doesn't list a time frame. It also seems it would be an up or down vote, and there doesn't seem to be a provision for a replacement vote.