Preheat oven to 350 degrees.
Pat chicken breasts dry with paper towel and sprinkle them generously on both sides with salt and pepper. In a 12 inch skillet, heat the oil over medium high heat. Place the chicken breasts in the pan and cook for 3-5 minutes without moving, until golden brown.
Using tongs, turn over the breasts and cook on the other side for another 3-5 minutes (depending on thickness of breast). Place chicken in a greased baking dish and keep warm in oven while the sauce is made.
In the skillet with chicken drippings, combine the white wine, lemon juice, lemon zest, and shallots. Cook over medium heat about 5 minutes, stirring so shallots do not burn. Add milk and dijon mustard. Allow sauce to reduce slightly. Season with salt and pepper. Remove from heat and stir in butter until melted. Add freshly chopped parsley. Pour over chicken and serve.