In a small bowl, mix the thyme, black pepper, garlic powder, cayenne and salt. Mix to blend.
Place the chicken on a large plate or platter. Drizzle with the oil. Rub to coat both sides of the chicken evenly with oil.
Sprinkle the reserved seasoning mixture over both sides of the chicken. Rub to coat evenly.
Cover with plastic wrap, refrigerate for at least 10 minutes for the seasoning to flavor the chicken.
Spoon the preserves into a small microwavable bowl and cook on low power in 15-second intervals until melted.
Stir in the mustard until well blended. Set aside.
Place the chicken on the grill and reduce the heat to medium. (If it is not possible to reduce the heat, cook the chicken away from direct heat.) Cook for 3 to 5 minutes per side, or until no longer pink and the juice runs clear.
Serve each breast with 2 1/2 tablespoons of the reserved sauce spooned over the top.