Butterfly the chicken breasts, then cut them in half. You should end up with 4 pieces of chicken.
In a shallow dish, whisk together the flour, salt, and black pepper. Dredge the chicken in the flour mixture and shake off the excess.
Heat the olive oil in a large skillet over medium-high heat. Add two pieces of chicken and cook each side for 2-3 minutes until golden brown and the inside is cooked through. Remove the chicken to a plate. Repeat with the other two pieces.
To the empty skillet, add the butter. Let it melt, then whisk in the flour. Cook for 30-60 seconds until the flour is golden brown.
While whisking constantly, add the chicken stock, white wine, lemon juice, and capers. Bring to a boil, then reduce to a simmer and cook for 2-3 minutes.
Add the chicken back to the skillet and cook for 30 seconds until the chicken is heated back up. Stir in the parsley. Enjoy!
Nutrition information is calculated using an ingredient database and should be considered an estimate.