A candle may have caused the fire, officials said.
The fire commander said neighbors who rushed to the scene shortly after midnight helped pull some of the victims from the burning apartment in the city's Rogers Park neighborhood.
Chicago Fire Commissioner Raymond Orozco said the six who died were all children of a woman who was hospitalized from injuries she suffered in the fire. The woman's three other children were also hospitalized, Orozco said.
The commissioner confirmed reports from neighbors that the family in the third-floor apartment had been without electric service for at least a month, and had been relying on candles for light.
"A candle in the front hallway appears to have started the fire, but that's only a preliminary finding," Orozco said. he also noted that there were no smoke detectors in the three-bedroom apartment.
"(There were) a total of 10 removals from this fire — nine children and one adult. Six of the children were in cardiac arrest," Orozco said. A sixth child died later Sunday.
The ages of the children range from 3-16, officials said.
The fatalities were identified as Kevin Ramirez, 3; Idaly Ramirez, 3; Suzette Ramirez, 10; Eric Ramirez, 12; and Natalie Ramirez, who was 15 or 16. The sixth victim had not been identified, CBS affiliate WBBM-TV in Chicago reports.
A friend of Natalie Ramirez said that the children's mother was originally from Mexico and that the family had been in the United States for at least 16 years.
"The community is in shock," a tearful Jasmin Lamb, 16, said as she lay pink and white carnations on the sidewalk near the apartment. "They were a nice, warm family. My friend never got into any trouble."
The fire broke out at about 12:20 a.m. on the third floor of a large apartment building, Fire Department spokesman Larry Langford said.
A passerby noticed smoke coming out of the apartment window and got help, said Cmdr. Will Knight.
"Then the mother came running out with one child in her arms, screaming to the neighbors that there were other children inside," Knight said. "They asked her how many, and she said eight."
A neighborhood man rescued one child after running up three flights of stairs and bursting into the apartment, witnesses said.
When firefighters arrived, they saw a child at a third-floor window, Langford said. That child was rescued by ladder.
Other firefighters went up the stairwell and found the children who died huddled in the apartment's front room, not far from where the fire is believed to have started, Langford said.
Witnesses said a neighborhood man ran up three flights of stairs and burst into the third floor apartment, where he rescued one child.
When firefighters first arrived they saw one child at a third floor window, Langford said. That child was rescued by ladder.
Other firefighters who went up the building's stairwell found a number of children huddled in the three-bedroom apartment's front room, not far from the spot where the fire was believed to have started, Langford said.