Heat oil in a large nonstick skillet over medium-high heat.
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 salt and pepper. Add chicken to pan; cook 4 minutes on each side or until done. Remove from pan. Add broth, wine, and lemon juice to the pan; reduce heat, and simmer 1 minute. Stir in the parsley and capers. Spoon sauce over chicken.