This is a tax question. I will add tags to get you a broader response.
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You will definitely owe tax to Illinois and will have to file an income tax return there because you are working in Illinois and earning your income from Illinois sources.
You will also owe tax to Ohio because you live there and are a resident of Ohio (there are some issues with residency requirements that might be worth exploring with your own tax consultant; however, the question is very fact-sensitive and doesn't lend itself to short answers online).
However, because you'll be paying tax to Illinois for income you earned in Illinois Ohio should provide you with some sort of a tax credit against your Ohio taxes to take into account the taxes you will have already paid to Illinois. There are some ins and outs to the actual amount of a credit you would get from Ohio, but as a very general rule you would end up paying about one level of tax on the income, at the higher of the rate in Ohio or the rate in Illinois.
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