They are going to lose. From the summary of argument:
"...although conferring an individually held right, the scope of the 2nd amendment's protection is circumscribed by its primary purpose of preventing federal disarmament of the militia."
1. The Second Amendment protects an individual right to possess a firearm unconnected with service in a militia, and to use that arm for traditionally lawful purposes, such as self-defense within the home.
(a) The Amendment’s prefatory clause announces a purpose, but does not limit or expand the scope of the second part, the operative clause.
If the Supremes know that circumscribing means limiting, Chicago is in trouble right out of the gate.