Begin by placing the chicken breast in a pot of boiling water. Cook thoroughly until the meat is fully done. Once cooked, transfer the chicken to a bowl of cold water to cool it down quickly and lock in moisture. After cooling, shred the chicken into thin, bite-sized strands using your hands or forks.
Next, prepare the vegetables. Julienne the cucumber and carrot into long, slender matchstick pieces for a crisp texture and a vibrant presentation.
In a large mixing bowl, combine the shredded chicken with the cucumber and carrot. Drizzle over the soy sauce, sesame oil, and rice vinegar. Sprinkle in the sugar and toasted sesame seeds. Toss everything together until well coated and evenly mixed.
Serve chilled or at room temperature, garnished with extra sesame seeds if desired. This refreshing salad is best enjoyed fresh.