Yes, there is indeed a branch of Kentucky Fried Chicken here in Astana, in the Mega shopping centre to be precise. For any doubters out there, below is a photo taken on the 7th of September 2009, with Anna sat in her pushchair.
Ooops, just re-checked the picture, and the yellow lighting of the fast food outlet sort of drowns out the KFC symbol. I tried playing with it in Photoshop, but to no avail. Anyway, the store is there, but no Burger King or McDonalds stores in Astana just yet, to the best of my knowledge.