Sprinkle chicken breast with salt and pepper. Place flour in shallow bowl and dredge chicken in flour, evenly coating both sides of chicken.
Heat oils in skillet over medium-high heat. Add chicken and cook 4-5 minutes per side, or until golden brown and cooked through. Remove chicken from heat and place on plate. Sauté onion until translucent and stir in chicken broth, lemon juice, lemon zest, and garlic. Cook 5 minutes, until it starts to thicken. Add heavy cream and continue to cook 1-2 minutes. Taste sauce and add salt to taste.
Place chicken breast back into pan and coat with sauce. Cook until heated through. Sprinkle with parsley.