Let us explain how to file a Chicago property damage claim and what kind of compensation you can receive to get your car repaired after an accident. To find out how to file an uninsured motorist claim in Chicago, Illinois, call Lloyd Miller Law Group at (773) 8388100.If the at-fault driver has no insurance coverage, the other driver can rely on underinsured or uninsured motorist coverage to cover accident-related damages. A skilled Chicago car accident attorney can help you get the coverage and compensation you need even if the other driver doesn't have insurance. Chicago uninsured motorist lawyer. Injured in an accident? Chicago uninsured motorist lawyer. Injured in an accident? Understanding uninsured and underinsured motorist coverage is crucial for all drivers. Illinois law requires you to report any accident involving injuries or even a small amount of property damage.