What kind of food does she like? You don't necessarily need a store like Trotters to go--you can pick up food to go almost anywhere.
Having said that, if you're looking for upscale picnic fare, I agree with the recommendation for City Provisions (1818 West Wilson Avenue) and would also add Publican Quality Meats (825 West Fulton Market) or Provenance (LOGAN SQUARE 2528 N. California Ave/ LINCOLN SQUARE 2312 W. Leland Ave).
"Knowledge is knowing a tomato is a fruit; wisdom is not putting it in a fruit salad." Miles Kington