In a large resealable plastic bag, combine the first four ingredients and ½ teaspoon of salt. Place chicken in bag, seal and turn to coat. Refrigerate 8 hours or overnight.
In a small saucepan, combine vinegar, water, sugar and remaining 1/2 teaspoon salt. Bring to a boil; whisk until sugar is dissolved. Remove from heat. Place carrots in a small bowl, pour vinegar mixture over top. Refrigerate 8 hours or overnight.
Drain and discard marinade. On a lightly greased grill rack, grill chicken, covered, over medium heat or broil 4 in. from heat until a thermometer reads 170°, 6-8 minutes on each side. Cool slightly; slice into strips.
Divide chicken among lettuce leaves, top with pickled carrots, green onions and cilantro. Sprinkle with coconut, if desired.