Reduce the heat to medium and add the capers, garlic, and the remaining 1 tablespoon oil to the pan. Cook, stirring, until the garlic softens and becomes fragrant, about 1 minute. Add the chicken broth and lemon juice, raise the heat to high, and cook, stirring, until the mixture reduces by about half, 3 to 4 minutes. Off the heat, swirl in half of the parsley and the butter and season with more lemon juice, salt, and pepper to taste. Drizzle the sauce over the chicken breasts
, sprinkle with the remaining parsley, and serve immediately.