You may be right about what other people do, but it's not legal. The money that you are paid for the days that you work in Chicago is Illinois source income. You have to file an Illinois nonresident tax return and pay Illinois tax on your Illinois source income. On your Indiana resident tax return you have to report all of your income, no matter where it is from. You will get a credit on your Indiana resident tax return for part or all of the tax that you pay to Illinois.
Your W-2 should have two lines of state information, one line for each state. The state wages in box 16 on each line should be the amount you earned for the time that you worked in that state.
Since you have to pay tax to both states, it would be helpful if your employer withholds tax for both states.
