Heat the oil in a large nonstick skillet over medium-high heat. Sprinkle the chicken with salt and pepper, and add to the skillet. Cook 5 to 6 minutes on each side or until well-browned. Remove to a plate. Cover and keep warm.
Add the garlic, mustard, cider and apples to pan; bring to a boil. Reduce heat, simmer, stirring often for about 5 minutes. Return the chicken and juices to the pan. Cook, stirring occasionally, until the sauce thickens and the chicken is cooked through, about 3 minutes.
Add the spinach to the pan, and toss until wilted, about 1 minute. Serve hot.