Article I, Section 10 is a little-known provision of the Constitution that prohibits states from passing a "law impairing the obligation of contracts."
Rahm Emanuel is not a state, but as mayor of a municipal subdivision of the state of Illinois, the constitutional provision applies to him too. Emanuel's letter to banks (and businesses) to stop doing business with gun manufacturers, etc. is a constitutionally prohibited third-party government impairment of private contracts between two private parties.
I supposes that's a matter of interpretation, but one might also argue that Emanuel's veiled threat also violates the First Amendment protection of speech and association.
Forget the legalities. Emanuel just trashed any attempt to attract a businesses and their jobs to Chicago. They've got enough problems already without having to deal with government wanna-be tin-pot dictators. I'm not for the sale of semi-automatic assault rifles, etc. but Emanuel has gone off the cliff on this one.
Below are some thoughts about the issue