The TV star – who ended her engagement with Luke Worrall in July amid speculation the model had cheated on her – is said to have enjoyed a series of low-key dates with the 'Gossip Girl' actor but is desperate to keep her new romance hidden.
A source said: "Kelly and Chace have been on a couple of dates and are trying desperately to keep things on the down low.
"Kelly is wary, she had zero confidence before she met Luke and look how that turned out.
"She wants to keep their romance out of the spotlight until she's sure it's the real thing. She's had a tough time of it since splitting from Luke.
"But she's looking great and is finally starting to feel that way too."
The 25-year-old star – who has shed more than 10lbs since splitting with Luke – has been impressing Chace with her outspoken views and wit.
The source added to website Mail Online: "Kelly is really unique and opinionated - something that Chace finds very cool - she also looks stunning but in a very unique and hip way, they could be Manhattan's new hip couple.
"Neither one of them are bothered about red carpets in a traditional sense, she grew up with all that debacle and he's a Texan boy at heart."
Kelly's parents are rocker Ozzy Osbourne and 'America's Got Talent' judge Sharon and she shot to fame on reality TV show 'The Osbournes'.