Place chicken breasts between 2 sheets of waxed paper and gently pound with a meat mallet or your fist to approximately 1/2 inch thick. Season lightly with sea salt.
Heat butter in a large, heavy nonstick skillet over medium heat until bubbly and starting to brown. Add chicken and cook, turning occasionally, until almost opaque in center and golden on both sides – about 5 minutes. Remove to serving plates.
Remove skillet from heat and let pan juices cool briefly. Add lemon juice, and parsley, stirring to loosen any brown bits in the pan. Spoon sauce over chicken and serve.
