The chapter at the Univ. of S. Carolina has a dessert called Kappa Delight, and the recipe is only given to alums. The seniors are given the recipe at the Senior Tea in anticipation of their impending alum status. It's a big deal--the seniors can hardly wait to finally get the recipe. I've made Kappa Delight for recruitment and other special occasions, but the chapter doesn't serve it for recruitment anymore (I think they might serve it at the Bid Day party though).
Kappa Delight is so absolutely scrumptious! It's chocolatey, gooey, and nutty--YUM!!! Funny thing, everyone's turns out a little differently--I think that's pretty neat and symbolic of our individuality.
I don't know of any food that is Kappa-specific though, and Kappa Delight is only done at our USC chapter as far as I know.