Translation:She is eating the chicken and the soup.
It is a little bit odd, sort of implies that she's eating both chicken and soup at the same time
Chick: A young bird, especially one newly hatched: "the cattle egrets hatched and reared two chicks" 1.1A newly hatched young domestic fowl: "dozens of fluffy, chirruping chicks hatched out"
Chicken: A domestic fowl kept for its eggs or meat, especially a young one: "rationing was still in force and most people kept chickens". Meat from a chicken.
Based on the dictionary headwords I would not equal a chick to a chicken.
The sentence may be unusual the but I assure you in the right context the English is fine.
Looks fine to me. Think context of a buffet, she has the coice of several dishes and she selects the chicken and the soup (there's obviously just one soup and just one dish with chicken).