Slice chicken breasts in half lengthwise.
Cover the breasts with wax paper and beat with mallet until thin.
In a small bowl, add flour, salt, and pepper. Mix well, and set aside.
Take each breast and dredge (coat) with the flour mixture. Shake off excess.
In a large saute pan or skillet add the butter and oil, and swirl to coat. Heat to medium.
Working in small batches, add two or three flour-coated chicken breasts to the skillet, cook for 3 minutes, turn and cook for another 3-4 minutes until lightly browned. Remove from pan, tent lightly with aluminum foil, and continue until finished.
Add chicken broth, lemon juice, and the cooked chicken (and capers, if using) to the skillet and sprinkle with parsley. Cook on low until reduced and the chicken reaches an internal temperature of 160 degrees.