Is there a statue of limitations for sexual abuse of a minor?

It depends on the circumstances.  The statute of limitations for charging a criminal offense begins at 720 ILCS 5/3-5 and continues on to 5/3-8.  There are many exceptions in it, which will apply depending on the specific factual circumstances.  As a general idea, the rule is "at least three years", "often ten years", and "there is no statute of limitations."  Which particular rule applies will depend on what occurred.