Yes, Illinois will allow you an "other state credit" for the taxes you pay to a non-resident state on dollars that are also taxed by Illinois.
The Supreme Court has ruled that it is unconstitutional for states to fail to provide credit for taxes paid to other states. (Comptroller of the Treasury of Maryland v. Wynne, 575 U.S. 542 (2015))
The ruling in effect outlaws double taxation by states.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
