As was rumored and hinted at, there is, in fact, a Persona 4 anime adaptation in the works, and you can check out its website here.
Besides the announcement, of course, the page features the "First Four" cast members of Chie Satonaka, Yukiko Amagi, Yosuke Hanamura, and the protagonist, who, interestingly, is called "Yu Narukami", rather than "Souji Seta", his name from the manga adaptation and the currently accepted "canon" name.
So far all the voice talents from the game will be reprising their roles, including Yui Horie (Bakemonogatari's Tsubasa, Kampfer's Akane) as Chie, Ami Koshimizu (Spice and Wolf's Holo, Code Geass' Kallen) as Yukiko