The investigation began at 5 a.m. at the restaurant in the 2700 block of Route 34, police said.
Police said they responded to calls of a person being stabbed. When officers arrived, they found an injured victim outside the restaurant.
Officers quickly placed the suspect into custody, police said.
SEE ALSO | New bollards installed at Oswego Portillo's after deadly crash into restaurant
As police conducted a "protective sweep of the restaurant," they found another stabbing victim dead. Oswego police said that victim was stabbed earlier, at around 3 a.m.
A witness to the attack outside the restaurant called police. The surviving victim's mother was nearby and tried to help. She spoke to ABC7 by phone anonymously.
"There were hitting each other," she said. "The guy got my son on the floor, so I got out of the car and I was trying to get him away from my son so he couldn't hit my son anymore."
When they arrived, police say a they found her son pinning the attacker down and they were able to take him into custody.
"Preliminary investigation indicates that the offender attacked one adult male victim at approximately 3:06 a.m. and another adult male victim at approximately 5 a.m. No restaurant employees were present at the time," said Cherese Spears with Oswego police.
Video obtained by ABC7 shows detectives at the Chick-fil-A. Crime scene tape was also seen surrounding a delivery truck, which is owned by a Rosemont-based company Martin Brower.
It is unclear if the delivery truck was involved in the incident.
Police are still investigating a motive for the attacks. The Kendall County Major Crimes Task Force has been activated to assist with the investigation and processing of the scene.
No other information was available.