So in these sorts of sentences, do you need to put the subject (chicken soup) right next to the verb? Seeing the answer makes me understand the child is not the subject, but part of an adjective phrase (if that's a proper grammatical term). But before seeing the answer, it is a difficult sentence to understand.
because in your sentence,
""The child eats spicy chicken soup" "
the verb is [eats], and "the child" is the subject.
But in this sentence,
"아이가 먹는 닭고기 수프는 매워요."
[매워요.] is the verb, or really, adjective/state of being. And the topic is the chicken soup.
The child eats spicy chicken soup would be 아이가 매운닭고기 수프를 먹어요.