It happened Sunday morning in Oak Lawn when police responded to a call of armed person at a home and a baby who was injured.
When they arrived, they performed CPR but the baby was pronounced dead at Advocate Christ Hospital.
"Praying for the family as well because it's gotta be a hard time for them, and they're just nice," said neighbor Carrie Lynn Hennessy. "I mean, they wave hello and never in the 11 years we've been here has there been police called or anything, so this is shocking for us, too."
Officers say the baby's parents left their child in the care of a relative and weren't at home.
That relative is now being questioned by police.