In a large skillet add broth and bring to a boil. Add chicken breasts, cover and cook, turning occasionally, until chicken is cooked through. Remove chicken from broth and shred.
In a small bowl, combine all dressing ingredients. Whisk until emulisified; set aside.
Make a bed of lettuce on individual plates; top with shredded cucumber. Place chicken over cucumber and sprinkle with ginger and cilantro. Drizzle with dressing and toss gently to coat. Serve immediately.