It will depend upon state negligence laws, if anyone was cited and who is found at fault in the accident as to who the driver of car #3 can place their claim with.

In some states the car causing the chain reaction will be held at fault for all of the cars that were damaged, while in other states it may be that each car is held responsible for the car they hit or the one that started the accident and the car that actual hit car #3 would both be partially responsible for the damage.

If the police cited only car #1 then it would likely be that driver that car #3 would place a claim with. If car #2 was also cited for say following too close then it may be one or both that is responsible. If the police came and took a report then the officer should be able to give their idea of who was at fault and try to guide the drivers about who they should place their insurance claim with.

If this situation has happened to you then you may want to check with your own insurance agent for advice on who the claim should be placed with according to state negligence laws. The consumer division of your state's insurance regulator may also be able to offer advice on the claims process in the multi-car crash.