Step 1In a large bowl, combine the brown sugar, chiles, garlic, galangal, cilantro, basil, green onions, lemongrass, lime zest and juice, coconut milk, sesame oil and fish sauce. Add the chicken pieces and toss to coat.
Step 2Place the chicken and marinade in a large, sealable plastic bag. Squeeze out the air and seal the bag. Place the bag in the refrigerator and marinate the chicken overnight, up to 24 hours.
Step 3Remove the chicken from the marinade and grill on an oiled rack over medium-high heat until the meat is firm and the juices run clear and a thermometer inserted reads 165 degrees. Place chicken on a platter and set aside for a few minutes before serving.