Translation:I like eating seasoned radish with fried chicken.
"~~ 하는 것이 좋아요": recommendation
무무침을 치킨하고 먹는 것이 좋아요. = You should eat radish with chicken.
"~~ 하는 것을 좋아해요": preference
무무침을 치킨하고 먹는 것을 좋아해요. = I like to eat radish with chicken.
치킨 does not always mean fried chicken. There are 바베큐치킨, 오븐구이치킨, etc. 치킨 just means cooked chicken. What is 무무침 anyway? Never heard of it. I think what everybody calls the radish served with chicken is 치킨무. I just call it 무.
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.
The "impersonal It" is often used to express one's opinion implicitly.
In English, this structure appears mainly in reports or academic works. In speech, it risks sounding "patronizing". Hence, translations of such sentences from Korean tend to revert to a more personal structure s.a. In my opinion; I think; I like etc.