Place flour in shallow dish. Dredge (cover) chicken in flour, making sure to evenly coat both sides of chicken.
Heat butter and oil in a skillet over medium-high heat. Add chicken and cook for approximately 4-5 minutes per side, or until it is golden brown and cooked through. Remove chicken from heat and place on a plate.
Pour in chicken broth and stir with wooden spoon, trying to stir in the browned bits on the bottom of the pan. Stir in chicken broth, lemon juice, lemon zest, and garlic. Cook for 5 minutes, until it starts to thicken. Add heavy cream and continue to cook for 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 Italian parsley.