Combine olive oil, paprika, brown sugar, lemon juice, and garlic in a large ziplock bag. Place chicken pieces in the bag. Massage marinade into chicken, seal, and refrigerate 24 hours.
Preheat the oven to 350 degrees F. Mix barbecue sauce and vinegar in a small bowl and set aside.
Remove chicken from bag and place on a baking sheet (line baking sheet with foil for easy cleanup). Season with salt and pepper. Bake for 40 to 45 minutes, or until chicken is cooked through and an internal thermometer reaches 165 degrees F. Turn broiler on high and continue to roast 3 to 4 minutes until skin blisters. Remove chicken from oven and rest 5 minutes.
Brush a layer of BBQ sauce on the chicken. Return to the oven and broil 3 to 5 minutes. Flip chicken and repeat, broiling until caramelizes. Remove from the oven and serve.
*Nutritional information is an estimate. Please consult a doctor or nutritionist for the most accurate nutritional info.