Pat chicken dry with a paper towel. Rub with olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper.
In a small saucepan, combine tomato sauce, tomato paste, apple cider vinegar, Dijon mustard, Worcestershire sauce, optional sweetener, smoked paprika, garlic powder, onion powder, chili powder, cayenne if using, and water.
Simmer sauce over low heat for 5 to 8 minutes, stirring often. Add a little more water if you prefer a thinner sauce.
Grill method: Preheat grill to medium heat. Grill chicken for 5 to 7 minutes per side, depending on thickness. Brush with barbecue sauce during the last 5 minutes of cooking.
Oven method: Preheat oven to 400°F. Place chicken in a lightly oiled baking dish. Bake for 20 to 25 minutes, brushing with sauce during the last 10 minutes.
Cook until chicken reaches an internal temperature of 165°F.
Let chicken rest for 5 minutes before serving. Spoon extra warm sauce over the top if desired.