Slice the chicken breasts in half widthwise.
Place them in between 2 large pieces of plastic wrap or in a large plastic zip bag and gently pound them with a mallet until they are about a ½” thick. Set aside.
Add the flour to a bowl and season very well with salt and pepper and mix together.
Coat the chicken breasts on both sides in the flour and pat off any excess flour. Set on a plate.
Add the olive oil to a large frying pan over high heat. Once the oil begins to very lightly smoke add in the chicken breasts and immediately turn the heat down to medium.
Cook for 4-5 minutes or until browned and halfway cooked through and flip over.
Turn the heat down to low and cook for a further 4-5 minutes or until cooked throughout.
Remove the chicken breasts and set aside.
Add the shallots and garlic to the pan where the chicken was cooked and saute for 1 to 2 minutes or until very lightly browned over low to medium heat.
Add in the wine, capers, and juice of ½ lemon and cook until the liquid is almost gone or about 1-2 tablespoons are left.
Remove from the heat and add in the butter and swirl the pan in a circular motion until completely melted.
Finish with parsley, 1 tablespoon of lemon juice, salt, and pepper and pour over the cooked chicken breasts and serve.