This law pretty much eliminates pistol hunters. Unless someone starts manufacturing pistol cylinders with only 3 chambers for revolvers. The Thompson Contender has been around for decades.

Bond Arms added the Cyclops to their derringer lines.

My brother has a Thompson Contender, it is a quality pistol. The Cyclops I am not familiar with. In any case these niche firearms are fine if you want to spend your money on single purpose firearm. But hundreds of other firearms are eliminated for no practical reason. A large bore revolver that can serve multiple purposes is not legal for hunting in Illinois for no real reason. There is no real difference between a three shot pistol and a six shot revolver for the purpose of hunting deer.
Who makes a three shot pistol? What kind of idiots drafted this legislation?