It's not Flossmoor, which is on a rectangular piece of land (mostly) running north-south.
From the angle of the road on the bottom (I presume south) of the photo, I was going to guess the Palos Hills course in the Cook County Forest Preserves, but the entrance for that was on the south end, and I see no entrance here. (The course was closed when the Manhattan Project's second reactor was built, replacing the one at the U of C during World War II.)
So, I dunno.