29-year-old Bana was born at the Brookfield Zoo in 1995 and arrived to the Lincoln Park Zoo in 2010.
Earlier this month, she was diagnosed with congestive cardiac failure and bronchopneumonia.
Although zoo staff tried to keep her healthy, they said a full recovery in her condition was not possible.
On Tuesday, veterinarians made the decision to euthanize Bana.
"Bana has left an undeniable mark on the hearts of zoo staff, volunteers, and visitors, and played an important role in her own troop," said Curator of Primates Jill Moyse. "Bana was not only a great mother, but she was very tolerant of her babies and other babies in the group playing on top of her. She loved spending time in the outside yard and sometimes could be seen foraging out there by herself."
During her 14-year stay, she was a part of the cognitive touch screen programs at the zoo's Regenstein Center for African Apes.
Bana was also the dominant female in the family gorilla troop, which is led by silverback Kwan.
The troop of her son Djeke, female Rollie and her son Mondika, female Bahati and her daughter Bella.
The troop visited Bana after her passing, just as they would naturally do in the wild, the zoo said.