The shooting happened around 2:25 p.m. in the 7400 block of South Euclid Avenue, in the South Shore neighborhood, Chicago police said.
The two men were involved in a physical altercation near an alley, which escalated to gunshots, police said.
A 36-year-old man was shot twice in the head, police said. He was pronounced dead at the the scene.
A 20-year-old man was shot in the leg and was taken to the University of Chicago Hospital, initially reported to be in critical condition, police said.
No one was in custody. Police continue to investigate.
INTERACTIVE SAFETY TRACKER Track crime and safety in your neighborhood