In a bowl or large resealable bag, whisk together the coconut milk (stirring it first), nam pla, lime juice, minced garlic, minced shallots, hot sauce, red pepper flakes, sugar, chopped cilantro, and a few grinds of black pepper until the sugar dissolves.
Add the chicken breasts to the bag or container, coat thoroughly with the marinade, remove excess air if using a bag, and seal.
Refrigerate and marinate for at least 4 hours, turning the bag occasionally; overnight marinating is recommended for deeper flavor.
Preheat your grill or grill pan to medium-high heat and oil the grates lightly to prevent sticking.
Grill the chicken, skin-side down first, turning as needed, until the thickest part reaches an internal temperature of 160ºF and the juices run clear.
Remove from the grill and let rest a few minutes, then serve with lime wedges for squeezing over the chicken.