There is currently no way to recall the Mayor of Chicago but a new state law would change that

From Ballot Access News:

Illinois Representative La Shawn Ford has introduced HB 4356 into the legislature. It provides a method for recall of the Mayor of Chicago. The legislature convenes on January 13, 2016. See this story. Currently there are no procedures for recall of state officials in Illinois, except there is a procedure to recall a Governor, passed by the voters in 2010.

The bill is prompted by ongoing protests against the current Mayor, Rahm Emanuel, who was re-elected in the spring of 2015. The bill would require the signatures of 15% of the last Mayoral vote, which at this time would be 88,610 valid signatures. If the voters voted in favor of a recall, only then would candidates to replace the Mayor be allowed to collect 12,500 signatures to run in a replacement special Mayoral election. And if no one gets 50%, there would be a runoff election. So the process would involve potentially three elections: (1) the recall election; (2) the replacement election; (3) a possible run-off.