M.L.
When we've traveled, I've noticed families with young children bringing their car seats and/or strollers along. You might want to call your airline (or get online) and find out if you will have to check the baby equipment or if it will be stowed away for you once you get on the plane.
Yes, there's always a chance of loss or damage to anything that goes on a flight. But there's never any publicity about the many pieces that fly without damage. All the same, do you have a friend or relative in Chicago who might be able to lend you a good car seat? There's no harm in asking around.