Preheat oven to 400°. In small bowl, combine the spinach, sun-dried tomatoes, goat cheese, garlic, ¼ teaspoon pepper and ⅛ teaspoon salt.
Cut a pocket horizontally in the thickest part of each chicken breast. Fill with spinach mixture; secure with toothpicks.
In an 8-in. cast-iron or ovenproof skillet, heat 1-½ teaspoons oil over medium heat. Brown chicken on each side. Place in oven; bake 10 minutes.
Meanwhile, toss asparagus with remaining 1-½ teaspoons oil, ¼ teaspoon pepper and ⅛ teaspoon salt; add to skillet in oven. Bake until a thermometer inserted in chicken reads 165° and asparagus is tender, 10-15 minutes longer. If desired, drizzle with vinegar. Discard toothpicks before serving.
