TRIM THE BEAN SPROUTS at both ends. Peel the cucumber, split it in half lengthwise and remove the seeds with a teaspoon. Finely shred the cucumber into 3-inch lengths. Peel and finely shred the carrots into 3-inch lengths. Set the vegetables aside. Take all the meat off the cooked chicken and shred it into fine strips using a sharp knife or cleaver.
Arrange the chicken strips on a platter and surround them with the bean sprouts, cucumbers and carrots. Combine all the ingredients for the dressing and mix them thoroughly. (I find an electric blender is useful for this, but you could use a screw-top jar and shake everything in it well.) Pour the dressing all over the chicken and vegetables and mix well. Serve at once.