The blaze broke out in the complex in the 1400-block of West Chase around 11 p.m. Monday.
Fire officials say it took nearly an hour to put the fire out.
Firefighters forced their way into an apartment and found a man overcome by heavy smoke.
"They found one victim on a couch," said Michael Kelly of the Chicago Fire Department. " [They] picked him up and took him out to the hallway and brought him outside the ambulance."
The man firefighters rescued stable Tuesday after suffering serious respiratory problems.
The American Red Cross dispatched a team to provide help for residents who had to evacuate their apartments.