Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/2-inch thickness using a meat mallet or rolling pin. Sprinkle chicken evenly with pepper and salt; dredge in flour.
Heat 1 1/2 teaspoons oil in a large nonstick skillet over medium-high heat. Add half of chicken; cook 3 minutes on each side or until done. Remove chicken from pan; keep warm. Repeat procedure with remaining 1 1/2 teaspoons oil and chicken. Add shallots to pan; sauté 1 minute or until tender. Add broth, lemon juice, and capers. Increase heat to high, and cook 1 minute. Stir in 1 teaspoon parsley. Spoon sauce evenly over chicken. Sprinkle with remaining 1 teaspoon parsley.