Almost certainly Yes.
Some border states to IL have reciprocal tax agreements with the other so that only one state tax form is required.......................BUT, IL and MO do not.
You file a non-resident MO tax return for just the MO wages...and an IL Resident tax return for All income from everywhere. IL allows a credit for taxes paid to MO, but you have to prepare the MO non-resident tax return before the IL Resident one.
Yes, you will have to file a nonresident Missouri return and then the Illinois resident return.
Please complete the nonresident return first to ensure correct calculations for you resident return.
Please see How do I file a nonresident state return?
So, my question about this is ... does this force me to purchase a second state module for my TurboTax Deluxe, because it only came with 1 state? That doesn't seem fair if I'm only filling out both returns because the state I did all the actual work in doesn't have a reciprocal agreement set up with the bordering one I live in.