Score the skin side of each piece of chicken 2 to 3 times, about 1/8 inch deep.
Whisk together the the juice of 1/2 lime, 1 tablespoon fish sauce, garlic, 1 tablespoon rice vinegar, Chinese five-spice powder, 2 teaspoons hot chile paste, ginger, and soy sauce in a bowl. Pour into a resealable plastic bag. Add chicken, coat evenly with the marinade, squeeze out excess air, and seal the bag. Marinate in refrigerator for 6 hours.
Preheat an outdoor grill for medium-high heat, and lightly oil the grate.
Remove chicken halves from the bag and transfer to a plate or baking sheet lined with paper towels. Pat chicken pieces dry with more paper towels. Reserve marinade mixture in a small bowl.
Whisk together the 1/3 cup rice vinegar, juice of 1/2 lime, 1 teaspoon fish sauce, and 1 teaspoon hot chile paste in a small bowl. Set aside.
Grill chicken, skin-side down, on the preheated grill for 2 minutes. Turn each piece, brush with reserved marinade mixture, and move to indirect heat.
Grill, brushing with glaze and turning ever 10-15 minutes, until well-browned and meat is no longer pink in the center, about 45 minutes total. An instant-read thermometer inserted into the thickest part of the thigh, near the bone, should read 180 degrees F (82 degrees C).
Drizzle vinegar lime juice mixture over the chicken and serve.
