Combine the first seven ingredients in a small saucepan; bring to a boil. Reduce heat; simmer, uncovered, for 5 minutes. Remove from the heat; stir in lime juice and peel; set aside.
Combine the chicken, dried cranberries, carrot, green onions, mint and basil in a small bowl.
Place about 3 tablespoons chicken mixture on each lettuce leaf. Top with 1 tablespoon cranberry sauce mixture and 2 teaspoons peanuts. Fold lettuce over filling. Serve with remaining sauce.
Makes 1 dozen.