Place chicken breast between wax paper and pound slightly with mallet. Sprinkle with salt and pepper. Heat 1 tablespoon oil and 1 tablespoon butter in skillet. Cook chicken over high heat for 4 minutes on each side. Transfer to warm serving platter. Add chives, lemon juice, brandy, parsley and mustard to pan. Cook 15 seconds, whisking constantly.
Whisk in broth and stir until sauce is smooth. Whisk in remaining oil and butter. Pour sauce over chicken and serve.