Boil chicken breast in boiling water until cooked.
Let the cooked chicken breast cool and shred it into small pieces.
Julienne cucumber and radish and set aside.
Prepare cold chogye noodle broth by mixing chicken broth, vinegar, mustard, sugar, and salt.
Boil somyeon (thin wheat noodles), rinse in cold water, and drain.
Place somyeon, chicken breast, cucumber, and radish in a bowl.
Pour the cold chogye noodle broth over and serve.