The fire broke out in a first-floor unit of an apartment building on the 900 block of East 86th Street. Calls for help came in just before 9 a.m., authorities said.
A female resident and her boyfriend, Lloyd Crenshaw, managed to escape their apartment on the second floor with the help of firefighters. Her brother and grandmother were trapped in the apartment below.
The 27-year-old man was found in the apartment's front room, but the 83-year-old grandmother was trapped in her bedroom.
The grandmother was transported to Trinity Hospital. The 27-year-old was taken to University of Chicago Hospital, where he later died.
Fire officials said there were no working smoke detectors in the apartment building.
Officials will return to the scene Friday to distribute information about smoke detectors, according to a Tweet from the Chicago Fire Department.
Officials said the fire was contained in the unit but caused damage to the whole building. An investigation into the cause of the fire is underway.