Boil the chicken breast in boiling water until cooked, then cool and shred it.
Julienne the radish and slice the cucumber thinly.
Cook the noodles, rinse in cold water, and drain.
Make the broth for the chogye noodles with vinegar, salt, sugar, mustard, soy sauce, and chicken stock.
Place cooked noodles, shredded chicken breast, radish, and cucumber in a bowl.
Pour the chilled broth to finish.