Place chicken breasts between two sheets of plastic wrap. Using a meat mallet, pound the chicken to 1/4 inch thickness. Season with salt and pepper.
Dredge the chicken in flour, shaking off any excess.
Heat olive oil and 2 tablespoons of butter in a large skillet over medium-high heat. Add the chicken and cook for 2-3 minutes per side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
Add the remaining 2 tablespoons of butter, garlic, and lemon juice to the skillet. Cook for 1 minute, stirring constantly. Add the chicken broth and bring to a simmer.
Return the chicken to the skillet and cook for 1-2 minutes, or until heated through. Stir in the parsley and serve immediately.