LeAndrea White was pronounced dead at the scene at 6:05 p.m., according to the Cook County Medical Examiner's office. An autopsy is scheduled for Thursday.
Chicago firefighters were told a child was trapped upon their arrival at the three-story, courtyard building on Wednesday afternoon. The child's body was found during a search in the third-floor unit.
Officials said the fire appears to have been contained to that one unit.
A mattress caught fire in the bedroom of an apartment in the 1700 block of West Juneway Terrace about 2:20 p.m., according to police and Fire Media Affairs Director Larry Langford.
Investigators think there were five people inside the unit -- which had no functioning smoke detectors -- and that they may have tried to use fire extinguishers in the apartment themselves before dialing 9-1-1, Langford said.
The girl's mother apparently tried to hoist the mattress out a window, increasing the intensity of the fire, according to Langford and Schona Buranda, who works with a local service group and spoke on behalf of the family that lived in the apartment.
"Tragically, the broken window let in an unlimited supply of oxygen, which most likely made it considerably hotter and stronger," Langford said.
The 3-year-old girl was found dead in the bedroom when firefighters arrived about 2:25 p.m., Langford said.
LeAndrea had been playing with matches or a lighter and accidentally set the mattress on fire, Buranda told the Chicago Sun-Times.
"She was a very bright kid, very smart and curious and active," Buranda said.
LeAndrea loved playing with cellphones. Her aunt, Vaddie Weekly, had snapped a cell phone photo of the toddler just the night before and posted it to Instagram.
"She had a lot of energy," Weekly said.
Two people were taken in good condition to Presence Saint Francis Hospital in Evanston with smoke inhalation, police said. Two others declined treatment.
The fire was extinguished by 3 p.m., and the apartment unit was deemed uninhabitable, Langford said. Red Cross officials were helping an unspecified number of residents find shelter.
Fire Department officials will visit the neighborhood Thursday to pass out smoke detectors and fire safety information in the wake of the fatal blaze.
The Sun-Times Media Wire contributed to this report.