The move was made without a pitch and is understood to have been prompted by the brand's desire to put more emphasis on customer relationship marketing.
Chemistry will now also take over the management of the Baileys.com global website, as well as oversee the brand's social media strategy.
Last month, Diageo announced that it was planning to consolidate its below-the-line marketing strategy across its portfolio of brands, which also includes Guinness, Pimm's and Smirnoff. Along with Chemistry, those affected include Agency Republic, AKQA, EHS 4D and Tullo Marshall Warren.
Agency Republic has worked on Baileys' digital account since February 2006, when it was appointed to handle the digital marketing strategy.
It added the global creative work in August that year and was responsible for launching the brand's first global website.
The agency's relationship with other Diageo brands, including Smirnoff, Jose Cuervo and Bushmills, is unaffected.
Chemistry first started working with Baileys in 2003 and is responsible for the brand's global relationship marketing.
In 2008, the agency developed "The Baileys Lounge", an online members' club that provided subscribers with special offers from the Baileys range.
Last month, Baileys handed its £40 million advertising account to Bartle Bogle Hegarty. The agency won the business after a pitch against Abbott Mead Vickers BBDO, Mother and Saatchi & Saatchi.