Officers responded to a call about a stabbing in the Albany Park neighborhood's 3700-block of West Leland Avenue just before 9 p.m.
Responding officers found a 46-year-old man, who had suffered multiple lacerations to his body, walking on the sidewalk.
The Chicago Fire Department treated him and took him to Illinois Masonic Hospital in fair condition, police said.
Another man, 40, was on the scene. Police said he also suffered multiple lacerations, and CFD took him to the same hospital in critical condition.
Police said the two men were arguing when they both took out cutting instruments and started fighting.
Neither man is in custody, and Area Five detectives are investigating.
Police did not immediately provide further information.
INTERACTIVE SAFETY TRACKER Track crime and safety in your neighborhood