To drive from Chicago, IL to Tampa, FL will take around 17 hours, depending on traffic.
There are three different routes you can take, but there is very little difference in terms of time of journey between the three.
Option A: 1,172 miles, 17 hours 38 mins, via I-65 S and I-75 S. This route will take you through Indianapolis and Louisville.
Option B: 1,142 miles, 17 hours 46 mins, via I-75 S, and goes via Terre Haute.
Option C: 1,209 miles, 17hrs 47 mins, via I-57 S, 1-24 E and I-75 S, travelling through Champaign, Mt. Vernon and Shawnee National Forest.
As there is hardly any difference in time, I would take option C as I would love to go to Shawnee National Forest. There are some great hikes and it would be a perfect place to camp for a night and break up the trip. It even has a little Grand Canyon known as, err, the little Canyon!
All routes meet in Nashville, TN, from where you will have about another 10 and a half hours before Tampa.