In a blender or large food processor, combine the garlic, serrano peppers, ginger, cilantro, lime zest, soy sauce, sugar and coconut milk. Process until smooth.
Place the chicken into a large resealable bag, and pour the liquid from the blender in with it. Seal, and refrigerate for about 1 hour, turning once after 30 minutes.
Preheat the oven's broiler.
Place the chicken onto a broiling pan, and pour the marinade into a saucepan.
Broil the chicken for about 10 minutes on each side, until browned and the juices run clear. While the chicken is cooking, bring the marinade to a boil. Simmer over medium heat for about 5 minutes, then remove from the heat.
Place chicken onto a serving plate, and pour the sauce over it to serve.
