I haven't played a ton of golf in Chicago, but I've never played a better of greens than at Chicago Golf Club. The sixth green there is incredible and might be my favorite in golf. The green on the short hole is amazing too.
Beyond that, I thought the greens at Old Elm were exceptional, and loved the 4th and the double green (6 and 17 I think), as well as 9.
Shoreacres are also outstanding as a set, and I found 3, 10, 12, 13 and 18 to be among the best of the bunch.
I've got some photos of the latter two courses and will post a few later.