Grilled or barbecued chicken is popular as a common street food and as a restaurant specialty across Thailand but the best and tastiest comes from Isan province where they take whole chickens and roast them butterflied down the middle.
Up to 4 hours prior to serving, make the dipping sauce. Heat vinegar to a boil in a small nonreactive pan. Add sugar, stir to dissolve it, then reduce heat and simmer for 3 to 4 minutes. Add crushed red pepper and minced garlic and simmer for 1 minute more. Remove from the heat and stir in salt. Pour into a serving bowl and let cool to room temperature before serving.
When ready to cook, combine garlic cloves, pepper, cilantro, ginger and pinch of salt in a large mortar or food processor or food mill and mash or pulse to a coarse paste.
Transfer to a large bowl. Stir in fish sauce and coconut milk. Add chicken and stir to coat with the marinade. Refrigerate, loosely covered, for at least 30 minutes and up to 1 hour.
Preheat grill to medium. Oil the grill rack using a folded paper towel coated in vegetable oil. Hold it with tongs and rub it over the rack.
Remove the chicken from the marinade, discarding marinade. Grill, turning occasionally, until golden brown and an instant-read thermometer inserted into the thickest part without touching bone registers 165 degrees F, 15 to 20 minutes.
Optional: Preheat broiler to high. Place chicken in a roasting pan, discarding marinade. and broil about 5 inches from the heat, leaving the oven door ajar. Check after 8 minutes or so; the chicken pieces should be browning. Turn them over and cook until an instant-read thermometer inserted into the thickest part without touching bone registers 165 degrees F, about 8 minutes more.