A car accident in which the other person has no insurance, you'll likely end up making an uninsured or underinsured motorist insurance claim. 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.To find out how to file an uninsured motorist claim in Chicago, Illinois, call Lloyd Miller Law Group at (773) 8388100. The attorneys at Aiello, Harris, Abate Law Group PC explain under insurance and uninsured motorist claims. Call (732) 253-4512. Uninsured motorist coverage, which motorists are also required to carry, covers bodily injury. Our Illinois car accident attorneys can help you navigate uninsured claims and underinsured claims. No fee unless we win. Attorneys at Malman Law will make sure that you get the just compensation. Can I Bring an Uninsured Motorist Claim without Bringing a Claim Against the At-Fault Driver?