When -하고 is used to show connection between two objects, it is normally used with the last object.

For example, I eat bread with milk. 저는 빵을 우유하고 먹어요.

The Korean word 치킨 is a false cognate. They borrowed this word from English and so it has a limited meaning in Korean. It only means fried chicken in Korean, whereas in English it can mean the bird or the meat raw or prepared in any of numerous different ways. My Korean students always make the mistake of saying that chicken is their favorite food, but they only mean fried chicken is their favorite food.