Preheat a grill to medium-hot or a grill pan to medium-low. Place the 3 tablespoons of oil in a medium saucepan over medium heat. Stir in the garlic and cook for 1 minute, then stir in the paprika and cook for 1 minute more. Add 1 cup of water and the ketchup, lemon juice, orange juice concentrate, brown sugar, Worcestershire sauce, mustard and cayenne pepper. Season the sauce with salt and pepper and simmer until slightly thickened, 8 to 10 minutes. Reserve half of the sauce to serve at the table.
Coat the chicken breasts with oil, wrap in foil packets, and grill for 3 minutes on each side. Brush some of the sauce on both sides of the chicken and continue grilling until cooked through and still juicy, about 3 minutes more per side. Serve with the reserved sauce.