Remove and discard skin and bones from chicken. Using two forks, pull chicken apart into shreds. In a large saucepan combine shredded chicken, the water, coconut milk, carrots, lime juice, soy sauce, 2 teaspoons Thai seasoning, and salt.
Bring to boiling; reduce heat. Simmer, covered, about 8 minutes or until carrots are crisp-tender.
If desired, top each serving with additional Thai seasoning, cilantro, and peanuts and serve with lime wedges.