While tornadoes can happen any time of the year, the tornado season really starts to ramp up in March in Illinois (see plot below) and remains active through the spring and on into summer. April, May, and June are the three standout months historically. So far 2015 has been very quiet with no severe weather reported in Illinois so far, according to NOAA.
You can see more plots like this on our tornado plots page.
Historical Tornado Tracks
On our tornado mapping page, you can see tracks by month and by county across Illinois. For example, here are the number of tornado tracks for March from 1950-2010.
The Midwestern Regional Climate Center took this concept to the next level, and the person who developed the original Illinois maps developed this cool interactive Tornado Track Tool (screenshot below).