Pat chicken breasts dry. Place each breast flat on a cutting board. With knife parallel to the board, cut the breast in half through the middle to make 2 pieces. Place each piece between 2 layers of plastic wrap. Pound with a mallet until ¼ inch thick.
In a shallow dish, combine flour, salt, and pepper. Lightly dredge chicken in flour mixture.
To a skillet over high heat, heat 1 Tablespoon olive oil until shimmering. Cooking in batches, add chicken breasts in one layer, adding oil as needed. Brown for 2-3 minutes on each side, or until chicken reaches 165F, then set aside.
Using the same skillet on medium heat, add wine and chicken broth and reduce for 2-3 minutes, stirring constantly to scrape the brown bits off the bottom of the pan. Stir in lemon juice, zest, and capers.
Change heat to low and add butter, stirring until melted. Season with salt and pepper to taste. Add chicken to skillet. Toss to coat and warm. Garnish with parsley and serve immediately.
Great with steamed broccoli and rice or noodles.
Notes
Keep leftover lemon chicken piccata in an airtight container in the refrigerator for up to 4 days.