Cut 1/2-inch deep slashes in the skin-side of each chicken half; 2 cuts in each breast, 2 in the thigh, and 1 on the leg; remove wing tips.
Whisk rice vinegar, barbeque sauce, and garlic together in large bowl. Place chicken in bowl and turn to coat chicken in the marinade. Arrange chicken halves, cut-side down, in the bottom of the marinade bowl, cover the bowl with plastic wrap, and refrigerate for 1 hour.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Remove chicken from bowl, pat chicken dry with paper towels, and discard marinade. Place chicken halves, skin-side up, on a plate and season with salt, pepper, paprika, onion powder, and cayenne pepper.
Cook chicken, skin-side down, on the preheated grill for 3 to 4 minutes. Turn chicken over, close the lid of the grill, and cook, basting with remaining barbeque sauce ever 6 minutes, until no longer pink at the bone and the juices run clear, about 35 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 165 degrees F (74 degrees C).