Yes, you can claim high school tuition for a education expense credit in Illinois.
Please read this Illinois Revenue document for more information:
http://www.revenue.state.il.us/Individuals/Credits/educationexpensecredit.htm
These expenses are not deductible at the federal level.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"