Heat olive oil and butter over medium heat in a large skillet.
Salt and pepper one side of chicken; place seasoned side down in the hot skillet and cook until browned and cooked through, about 5 minutes on each side. Remove to a plate.
In the same skillet add sliced apples, brown sugar, and grainy mustard to the same skillet; toss to combine. Cook over medium heat 3 - 4 minutes or until the apples are tender and saucy. Stir in chicken. Serve over rice or mashed potatoes to soak up the sauce.