There are reports that the person being questioned is a teenager, and that witnesses have picked him out of a line-up, but authorities will only confirm that they have a person of interest. No charges were filed late Sunday.
The shooting happened at about 5 p.m. Saturday near 87th and King Drive in a parking lot used by Church's Chicken and A Piece of Cake bakery in the Chatham neighborhood.
The victims, all in their 20s, were apparently looking forward to a big birthday celebration for Chanda Thompson's 2-year-old daughter Sunday. They had just picked up a birthday cake for the party from A Piece of Cake when a gunman opened fire on their car.
"I was in an office, getting ready to leave when I just heard gunshots. There were like six of them, back to back," said Jennifer Lias, a witness.
One of the victims, Chanda Thompson, 21, was a student. Another victim was identified as Cortez Champion, 21. The other male victim has not been idenitifed but is believed to be Thompson's boyfriend. Witnesses say the gunman fled on foot. Two of the victims died at the scene. Another died at an area hospital.
"She loved her family," said Thompson's friend Camille Williams. "It is such a tragedy that she was murdered and she left behind a 2-year-old baby."
On Sunday night, community activists were passing out out leaflets, hoping to find witnesses to come forward with more information about the suspect and the car he was driving. They also want to bring more attention to the crime. Police suspect the gunman was targeting one of the two men in the car.
Victims' friends, neighborhood residents and anti-violence advocates say the bloodshed must stop.
"We want people to see that this is not acceptable. This isn't normal, and we can't get use to it. We have to make noise, we have to be loud and we have to let the city know this is not a South Side proble, this is not a West Side problem -- this is a Chicago problem, and we need people to stand up and make some noise about it," said anti-violence advocate Joy McCormick.
Earlier this spring, A Piece of Cake bakery hosted former Mayor Richard Daley, presenting him with a birthday cake in honor of his farewell tour of the city.
Making this all the more painful, Thomspon's aunt Charlene Davis is a well-know activist who works to try to prevent this type of violence.
"We march to prevent things from happening like this, and when it happens to your loved one, it's a low blow," Williams said.
Thompson's daughter turned 2 years old Sunday. Trying to keep things as normal as possible, ABC7 was told that Thompson's family went ahead with the child's birthday party as planned.