Put the chicken breasts in a saucepan and cover with cold water. Bring to a boil, reduce heat to a simmer and poach for about 15 minutes.
Combine the lime juice, fish sauce, sugar and pepper in a bowl and whisk with a fork until the sugar has dissolved. Add the onion and stir, then set aside.
Drain the chicken and let cool a bit, then shred. In a salad bowl combine the chicken, cabbage, carrots, mint and coriander. Pour over the dressing and toss. Sprinkle with peanuts and serve.