Place each piece of chicken between 2 sheets of wax paper; flatten to 1/4-inch thickness using meat mallet or rolling pin. (Or buy thin sliced chicken breasts!)
Combine flour, salt, and pepper. Dredge chicken in flour mixture.
Melt butter in a large skillet over medium heat and add olive oil. Add chicken and cook 3 to 4 minutes on each side or until golden brown.
Remove chicken and drain on paper towels and keep warm.
Add lemon juice, chicken broth, and lemon slices to skillet. Cook until thoroughly heated.
Pour lemon mixture over chicken. Sprinkle with parsley.