Sprinkle chicken with 1/4 teaspoon salt and pepper. Heat a skillet over medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Add chicken to pan; cook 5 minutes. Turn chicken over. Add wine, capers, garlic, and thyme to pan; cook 2 minutes. Add remaining 1/4 teaspoon salt, remaining 2 tablespoons oil, and stock to pan; bring to a boil. Reduce heat to medium; cook 8 minutes. Remove pan from heat. Stir in lemon juice and butter. Sprinkle evenly with parsley.