Kelly Davis, Dad, Rescues 2-Year-Old Daughter Myla From Kidnapper (VIDEO)

Two-year-old Myla can't sleep well. And if a man comes too close to her, she says, "Bad man, bad man," her dad Kelly Davis told the Chicago Tribune.

Given the kind of terror that this Zion, Ill., toddler and her family went through, her reaction is understandable.

Davis stopped an attempted kidnapping of Myla on Saturday night, and then chased the suspect through the streets of Chicago.

At 9:30 p.m., Myla and her 4-year-old sister were sliding off Daley Plaza's Picasso sculpture, a popular play site for kids. A man grabbed Myla by the arm, declaring her to be his daughter and calling her "Goldilocks," according to reports. He insisted that Davis, who was already positioned between Myla and the would-be abductor, get out of the way.

Davis, 31, told CBS News (video above) that the suspect challenged him to fight and threw a punch. Davis followed with a hockey-style shoulder-check, and the man fled. But the drama didn't end there.

Leaving his girlfriend, Amanda Green, to watch their children, Davis pursued the man for 30 minutes over several blocks before finally being able to flag down the police, outlets reported.

The suspect, James Gates, a 55-year-old with armed robbery and drug possession on his rap sheet, faces kidnapping and battery charges.

In another brazen child-snatching attempt earlier this summer, a stalker lifted up a 10-year-old girl walking in South Philadelphia, then dropped her as she fought back while the girl's 2-year-old brother reportedly screamed. The incident was captured on surveillance tape, leading suspect Carlos Figueroa-Fagot to turn himself in, NBC reported.

In that case, there was no adult caregiver present. Davis pondered what would have happened had he not been vigilant.

"I have no doubt that if I had my back turned, he would have grabbed her and she would have been gone in the city and I would have never seen her again," he told the Tribune.