Preheat your grill to medium-high heat (about 375°F to 400°F).
In a small bowl, mix together the salt, black pepper, garlic powder, and onion powder. Rub this spice mixture all over the chicken pieces.
In a medium saucepan over medium heat, combine the ketchup, apple cider vinegar, brown sugar, Worcestershire sauce, Dijon mustard, smoked paprika, and cayenne pepper. Stir well and bring to a simmer. Cook for about 10 minutes, stirring occasionally, until the sauce thickens slightly.
Place the chicken on the grill and cook for about 25-30 minutes, turning occasionally, until the internal temperature reaches 165°F.
During the last 5 minutes of grilling, brush the chicken with the homemade BBQ sauce, allowing it to caramelize slightly.
Remove the chicken from the grill and let it rest for 5 minutes before serving.