Trim the chicken of any fat. Place in a saucepan and cover with cold water. Bring to the boil then turn the heat down and simmer gently until just cooked through, about 5 minutes. Remove and discard the water. Shred the chicken with a fork.
Place the chicken in a large bowl with the cabbage, onion, mint and coriander. Toss.
In a bowl, whisk together the sugar, fish sauce, lime juice and vinegar (you can adjust quantities to taste). Pour over the salad and gently toss. Serve.