Governor Pat Quinn said he will leave the decision on whether to appeal up to the attorney general, who is considering it.
Mayor Rahm Emanuel says the court's decision is dangerous.
"This ruling runs counter to, not only common sense, but what every police chief in the country says, which is we should not allow more guns on the street," said Emanuel."
"We want to get the very best law that protects public safety," said Quinn. "That's where I'm coming from, and I'm gonna insist on that."
Quinn adds that there must be reasonable restrictions on concealed carry.