With abundant sunshine heating-up the very warm humid air mass in place, cumulus clouds could build into a few thunderstorms across the Chicago area this Sunday afternoon/evening. The best chance of storm development looks to be along a frontal boundary oriented northwest-southeast from westernmost portions of our area to well south of the city.
The National Storm Prediction Center thunderstorm outlooks have about a 40% chance of thunderstorms within 12 miles of a given location depicted in this most-likely area depicted on the maps below (light blue-shaded areas). This may be on the high side probability-wise, but does lay out the area with the best chance of t-storms.
Storms should die out for the most part as we reach the evening hours.