Illinois is a bit different when it comes to CCW licenses and reciprocity. To make a long story short, nonresidents are not able to obtain an IL CCW permit and IL does not offer reciprocity. Wisconsinites who hold a valid Wisconsin CCW permit can, however, drive through Illinois with a loaded weapon concealed in the car, but the weapon cannot leave the car.
Illinois is among the most restrictive states when it comes to concealed carry (and also has some of the worst crime rates…coincidence?). It does not have reciprocity with other states and (essentially) will not issue carry permits to non-residents.