The parents of 2-year-old Mekhi and Makayia Nash say the twins were left in front of a house Friday night in the 7100-block of Normal Avenue.
The temperature was around 15 degrees.
A resident at the home says the driver honked the horn and said the children belonged to a relative there.
Ida Brown lives at the home where the toddler's were dropped off and contacted police
"The little girl she started to tear up a little bit," Brown said. "So the neighbor across the street, she kinda went and talked to her and comforted her a little bit. When I asked the little girl you know your mommy's name? She said mommy. So that goes to show you how young these children were."
The children's parents said they were getting conflicting messages from the owner of Angels Aboard Daycare. The business is run out of a home in the 9400-block of South Parnell.
The parents, who don't own a car, said the owner at first said the children were with her and then stopped returning phone calls
It wasn't until a relative saw the toddlers' pictures in a Facebook posting that their parents went to police.
"I can't understand how he dropped them off at somewhere and not know where he dropped them off at," said the twins' mother, Lanicka Taylor.
The parents contacted police after a relative saw the toddlers' pictures in a Facebook posting.
"I really am at a loss for words," said the father, Michael Nash. "But I can say thank you Jesus, though. For real."
The children were briefly in the custody of DCFS while an investigation is underway into Angels Aboard Daycare. DCFS said the owner, Yvette Wilcoxon, is properly licensed.