There is a parking lot on 55th Street just east of Cicero that is $8.00 per day. They have a shuttle that runs all day/night going back & forth to the main terminal. The bus leaves you off at on the lower level in baggage claim.
I have never waited more than 4-6 minutes, coming or going. The lots have little huts to wait in.
We have used it several times & it works for us.
I miss ATA out of Midway.