1. Heat 4 qts to boiling in a 5 to 6 qt pan. Add chicken, cover and remove from heat. Let stand until chicken is no longer pink, 20-30 minutes. Transfer chicken to a plate and let cool.
2. Preheat the oven to 350 degrees. Toast coconut in a pan until golden, 4 minutes. Let cool.
3. Combine lime juice, sugar, fish sauce, chiles and oil in a large bowl. Tear chicken into bite size shreds, toss with dressing. Just before serving, gently mix in herbs and berries. Pile on plates and top with coconut.
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