The 21-year-old socialite was shopping in Camden Stables, in north London, when she allegedly took a £70 dress off a hanger in the Vintage King boutique and ran out of the store.
Peaches - the daughter of Boomtown Rats singer Bob Geldof - was recognised by a shop assistant who called the police.
A source told The Sun newspaper: "The assistant says she recognised Peaches as she came in. She says she saw Peaches rip the dress from a hanger and run out of the shop with it. It was apparently very blatant.
"The assistant ran after her but didn`t want to leave the shop unattended."
Police have confirmed they are investigating the claim, but a spokesman for the `OMG! With PeachesGeldof` presenter has denied the allegation.
He said: "Peaches knows nothing about any allegation of shoplifting and has not been contacted by police."
This is not the first time Peaches has been accused of stealing. She has previously been involved in three alleged shoplifting incidents but has avoided prosecution by paying for or returning the goods in question.
The source added: "There have been a number of misunderstandings over Peaches leaving shops without paying.
"The shop owner feels that just because she is the daughter of a rock star it doesn`t mean she shouldn`t have to face the law like everybody else."