Vietnamese Chicken Salad

Stir together lime juice, garlic, ginger, chiles, 2 teaspoons salt, and 1/2 teaspoon pepper, then rub all over chicken, inside and out. Marinate, covered, at room temperature while cooking vegetables. Thinly slice cabbage with slicer. Cut carrots into thin matchsticks (1/8 inch) with a knife. Cook vegetables in a large pot of salted boiling water (2 tablespoons salt for 6 quarts water) until crisp-tender, 4 to 5 minutes. Transfer to a large sieve or colander with a slotted spoon (return water to a boil) and rinse under cold water to stop cooking. Drain well. Add sugar to boiling water, then add chicken with marinade and cook, covered, 15 minutes. Remove from heat and let chicken stand in cooking liquid, covered, 30 minutes. Carefully transfer chicken with tongs to a cutting board and let stand until cool enough to handle. Coarsely shred meat (and skin if desired), transferring to a large bowl.