Score skin side of each piece of chicken 2 to 3 times, about 1/8-inch deep. Set aside.

Whisk garlic, juice of 1/2 lime, 3 teaspoons fish sauce, 1 tablespoon rice wine vinegar, Chinese five-spice powder, 2 teaspoons hot chile paste, ginger, and soy sauce together in a medium bowl until well combined; pour marinade into a resealable plastic bag. Add chicken, coat with marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator for 6 hours.

Preheat an outdoor grill for medium-high, indirect heat and lightly oil the grate.

Remove chicken from marinade, shake off excess, and transfer to a plate or baking sheet lined with paper towels. Pat chicken dry with paper towels. Reserve marinade in a small bowl.

Whisk together 1/3 cup rice wine vinegar, remaining juice of 1/2 lime, remaining 1 teaspoon fish sauce, and remaining 1 teaspoon hot chile paste in a small bowl until well combined. Set vinegar-lime mixture aside.

Grill chicken, skin-sides down, on the preheated grill for 2 minutes. Flip chicken, brush with reserved marinade, and move to indirect heat. Continue grilling, brushing with marinade, and flipping every 10 to 15 minutes, until 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 but not touching the bone, should read 165 degrees F (74 degrees C).

Drizzle vinegar-lime juice mixture over chicken to serve.