Yes, you will get a credit on you PA resident tax return for your IL nonresident state taxes.
You will need to file as non-resident for IL (for your IL source income only). You will also need to file a PA resident state tax return (for all income from all sources including IL). You will get a state tax credit in PA for the IL state taxes that you paid on your nonresident Il state tax return. Usually these state tax credits are listed on one of the last screens under the resident state's income tax information sections.
You will want to work on your non-resident IL state tax return first. You will then take a tax credit from your non-resident IL return on your resident PA state tax return. (Please note that you will only get a tax credit for your IL state taxes up to the amount of PA taxes that would have been paid if the income was earned in PA).
Just follow the TurboTax guide when working on your states (remembering to do your non-resident state return first) and TurboTax will do all the calculations and credits available for your resident states return.
Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment).
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