The man burst into the restaurant at 03:25 (08:25 GMT) in the suburb of Antioch and opened fire with a semi-automatic rifle.
Two other people were wounded. One of them wrestled the weapon from the man, who then fled the scene on foot.
Police are hunting for the suspect, whom they identified as Travis Reinking, 29, from Illinois.
James Shaw Jr, the customer credited with saving lives by taking the gun off the killer, has told US media he does not feel like a hero because "it feels selfish".
