Coat the chicken; first, place your chicken on a cutting board. With a sharp knife, butterfly your chicken, then cut it in half so you have four pieces. Season the chicken with salt and pepper, to taste.
Add the flour into a large zip-lock bag. Add your chicken pieces to the bag. Close the bag and shake vigorously until the chicken is coated completely. Remove the chicken from the zip-lock bag, gently shake to remove excess flour, and place it on the wire rack or a clean plate.
Cook the chicken:
Heat your oil; add 2 Tablespoons of unsalted butter and 2 Tablespoons of olive oil in a large skillet. Heat it over medium-high heat until the butter is melted.
When hot, add two chicken pieces, and make sure they do not touch.
Cook the chicken until golden brown on all sides, or 3 minutes per side. Remove the chicken from the skillet and set aside.
Melt another 2 Tablespoons and add the remaining olive oil to the same skillet. When hot, cook the remaining chicken pieces until golden brown. Remove the chicken from the skillet and set aside.
Add the garlic and cook for 30 seconds or until fragrant. Add chicken stock and deglaze the skillet, scraping any brown bits.
Add lemon juice and capers or olives along with the cooked chicken. Simmer the chicken for another 5 minutes.
Remove the chicken from the skillet onto the serving plate.
Add the remaining butter to the skillet and whisk vigorously until the sauce is emulsified.
Pour the sauce over the chicken.
Serve:
Garnish the chicken with chopped parsley and serve.
Notes
If you’re out of capers or simply not a fan, chopped green olives make an excellent substitute. Like capers, green olives are brined, which gives them that distinctive salty, tangy flavor.