Trim the fat off the chicken breasts and slice in half. Cover with plastic wrap so you don't contaminate the kitchen. Use a meat mallet to pound the pieces to about 1/4 inch thick.
Add the flour to a shallow container like a plasticware container. Season each piece of chicken with salt and pepper. Dredge each piece of chicken in the flour and set aside on a plate.
Heat the olive oil and 1 tablespoon of butter in a medium to large skillet. Place the chicken in the skillet and cook each side for about 4-5 minutes.
Pour in the lemon juice, white wine, and chicken stock. Allow the liquid to boil and reduce by about half, about 5-7 minutes.
Add in the remaining tablespoon of butter and most of the parsley and stir together for about 1-2 minutes. I reserve about 1 tablespoon of parsley for a garnish along with sliced lemon pieces.
Boneless Skinless Chicken Breast is usually sold 2 per package and average 1-1/5 pounds. So this recipe is for 1 package of chicken.