Put the chicken breasts in a bamboo or other steamer set over a large pan of simmering water. Cover and leave to steam for about 8 minutes or until the chicken is cooked through. Alternatively, poach the chicken for 8–10 minutes until the meat is cooked and tender.
Meanwhile, make the dressing by mixing together the ingredients in a bowl.
When the chicken is cool enough to handle, cut or tear it into strips and mix the pieces with 2 tablespoons of the dressing. Leave to cool.
Toss all the vegetables and herbs together and arrange in serving dishes. Scatter over the cold chicken and serve immediately with the remaining dressing.