Your employer should withhold tax for Indiana. You will have to file two state tax returns, an Indiana nonresident tax return and an Illinois resident tax return. You have to pay Indiana tax on the income you earn in Indiana. Since you live in Illinois, all your income is subject Illinois tax, no matter where the income is from. But you will get a credit on your Illinois tax return for part or all of the tax that you pay to Indiana. Prepare your Indiana nonresident tax return first, then your Illinois resident tax return, to make sure that the credit is calculated correctly.
You might still have to pay some tax to Illinois, if Indiana tax rates are lower than Illinois, or if you have significant income from sources other than the job in Indiana.