Spread the flour on a piece of wax paper and dredge each chicken breast.
Melt the butter and oil in a skillet. When it foams, add the chicken, and cook over medium-high heat for about 3 minutes on each side. Remove to a warm platter.
Pour off all but 2 tablespoons of fat from the pan, and stir in the lemon juice and salt and pepper to taste. When it is very hot, spoon this sauce over the chicken and sprinkle with parsley.