The 23-year-old star - the daughter of former drug addict and alcoholic Ozzy Osbourne - claims she suffered her first case of alcohol poisoning during a night out with 'The Simple Life' star.
Kelly told friends while partying with Paris at Las Vegas nightclub Noir last week: "Paris gave me my first alcohol poisoning!"
According to the New York Daily News newspaper, Paris was then overheard laughing: "I did?! That's hot!"
Kelly checked into rehab in 2004 to be treated for an addiction to painkillers.
Her 22-year-old brother Jack has also been treated in rehab for alcoholism, class A drug addiction and abuse of prescription drugs.
Their mother Sharon Osbourne has previously accused singer Courtney Love of introducing Jack to drugs when he was just 15. The former Hole singer has vehemently denied the allegations.