Slovak Restaurant in Chicago
As drasmino mentioned, Klas (in Cicero) is a good bet. Very cool old world decor and service. Despite the name, Czech Plaza (in berwyn) is another Slovak restaurant (at least they have pictures of Bratislava on the wall). The Bohemian Crystal in Westmont, is not in the same class as Klas, but is a great value.
Czech Plaza Restaurant
7016 W Cermak Road
Berwyn, IL 60402
639 Blackhawk Dr, Westmont, IL 60559
5734 W Cermak Rd, Cicero, IL 60804