Trim all visible fat and undesirable membranes from chicken breasts. Cut each one in half to make two pieces about the same size.
One at a time, put pieces inside a heavy Ziploc bag and pound chicken with a meat mallet or something heavy to make it an even 1/2 inch thick.
Season chicken with a small amount of salt, pepper, and poultry seasoning.
Chop parsley and set aside. Rinse the capers and pat dry with paper towels.
In a 12-inch nonstick frying pan, heat olive oil over medium-high heat. When oil is hot, add capers and fry until they open slightly and crisp a little, took 60-90 seconds for me. Remove pan from heat and use a spoon to transfer capers to paper towel, letting the oil drip back into pan.
Get oil hot again, then sauté chicken on top side until nicely browned, about 3-4 minutes. Turn over and cook on other side until chicken is done, probably only 1-2 minutes on the second side, but be sure chicken is cooked through.
Arrange chicken on serving dish with the most browned side facing up.
While chicken browns, measure out chicken stock, garlic, butter, and lemon juice so they’re ready.
Add garlic to hot pan and cook 15-30 seconds. Add chicken stock, and scrape pan to dissolve browned bits. Cook until stock is reduced by half, about 2 minutes.
Stir in lemon juice, then turn off heat and add butter, stirring until butter is melted. Add half of capers and parsley to sauce, then pour sauce over chicken, garnishing with remaining capers.
