Pretty sure they carry Daikon at Whole Foods and I'm reasonably sure you'll find it at any asian market on Broadway or Argyle that carry fresh veg. So Broadway Supermarket, Tai Nam or Viet Hoa should all have it. Just a quick red line ride away.
Broadway Supermarket
4879 North Broadway, Chicago
(773) 334-3838
Tai Nam
4925 N. Broadway
Tel: 773-275-5666
Viet Hoa
1051 West Argyle Street
(773) 334-1028
"Knowledge is knowing a tomato is a fruit; wisdom is not putting it in a fruit salad." Miles Kington