The Boeing 767 bound for Miami experienced an "uncontained engine failure", officials involved in the investigation said.
The pilot aborted the take-off and evacuated everyone on board via emergency chutes as black smoke billowed from the plane.
Twenty people suffered minor injuries, the fire department said.
Nine crew members and 161 passengers were on board.
A federal official quoted by the Associated Press news agency said the plane appeared to have suffered a rare and serious type of engine failure in which parts break off and are spewed outside the engine.
Passengers reported an explosion followed by flames and black smoke as the plane was speeding down the runway.
Sarah Ahmed said everyone on the right side of the plane rushed from their seats and moved to the left side.
"People are yelling, 'Open the door! Open the door!' Everyone's screaming and jumping on top of each other to open the door," she told WLS-TV.
"Within that time, I think it was seven seconds, there was smoke in the plane and the fire is right up against the windows, and it's melting the windows."
The incident took place at 14:35 local time (19:35 GMT).
An initial statement by Federal Aviation Administration (FAA) said the plane had burst a tyre, but that information was later deleted from the statement.
Why do people grab their bags after a plane crash?
American Airlines said passengers who still wanted to travel had been put on another flight to Miami.
Elsewhere, a FedEx plane caught fire at Fort Lauderdale, Florida, airport after its landing gear collapsed on landing, the FAA said.

Barbara Stensland, 43, from Cardiff, went to Carmarthen on 5 August.
When she tried to get a taxi from the railway station to the venue, less than one mile (1.6km) away, she was refused.
Carmarthenshire council's senior licensing officer, Justin Power, said: "We will investigate this matter and take any necessary steps."
Ms Stensland told BBC Radio Cymru's Post Cyntaf programme it took her more than an hour to reach the venue.
She said: "I went to the first taxi in the queue outside the station, I told him where I wanted to go.
"He laughed. I thought he was just joking along because I knew it was a fairly short distance.
"When I said 'seriously, can I get in the taxi?' He said 'no, I'm not taking you.' So he pointed me helpfully in the right direction and told me to walk."
Urtha Felda, from MS Society Cymru, said: "We have heard of people having trouble getting taxis.
"If somebody's still walking you can't see that they're disabled - if someone's in a wheelchair it's really obvious.
"It's not obvious, so I would say to people - don't make judgements."

US-based golf course designers Mike Keiser, Bill Coore and Todd Warnock have proposed creating the course at Coul Links, near Dornoch.
Four conservation charities have joined forces to oppose the project.
The developers said they were aiming for "minimal intrusion on the landscape".
The Scottish Wildlife Trust, RSPB Scotland, Buglife and Plantlife have concerns the course will result in the loss of a protected sand dunes habitat and rare wildlife.
The developers, who have held two meetings in the local area as part of public consultation on the plans, said the building of the course would involve laying turf over less than 55 acres (22ha) within a Site of Special Scientific Interest (SSSI).
SSSIs are areas indentified as having a diverse range of wildlife and geology.
The developers said their planned new course, close to Embo, would compliment nearby Royal Dornoch golf course and others in the East Sutherland area.
Mr Keiser, who owns Bandon Dunes Golf Resort in Oregon, said: "This is a wonderful opportunity to deliver a spectacular championship links golf course which represents all that is natural about golf, in the home of golf.
"Our golf course developments aim for minimal intrusion on the landscape and the utmost care and respect for the environment.
"Our team of environmental advisors is ensuring complete sensitivity to the land, and its location."
An American Airlines plane has caught fire on the runway of Chicago's O'Hare airport while taking off.
[NEXT_CONCEPT]
A woman with multiple sclerosis has said she was refused a taxi to a meeting of the MS Society because the journey was too short.
[NEXT_CONCEPT]
The developers of a planned 18-hole championship golf course have sought to allay concerns about their proposal's impact on a protected coastal area.