Pound the chicken breasts to an even thickness of about 1/2 inch, then season generously with salt and pepper. Prepare a shallow dish with flour and dredge each piece, shaking off excess to ensure a light coating.
Heat olive oil and butter in a large skillet over medium heat until shimmering and the butter starts to foam. Carefully place the chicken breasts in the pan, cooking for about 3-4 minutes on each side until golden brown and cooked through. Transfer the cooked chicken to a plate lined with paper towels to rest.
Add the minced garlic to the same skillet and sauté for about 30 seconds until fragrant, with a gentle sizzle and aroma filling the air. Scrape up any browned bits from the bottom of the pan with a wooden spoon.
Pour in the white wine or chicken broth, using a spoon to deglaze the pan and loosen the caramelized bits. Let it simmer for 2-3 minutes until reduced slightly and aromatic.
Stir in the freshly squeezed lemon juice and the rinsed capers. Continue simmering for another 2 minutes until the sauce thickens slightly and turns glossy, filling the kitchen with bright, citrusy scents.
Return the cooked chicken to the skillet, spooning the sauce over the top. Cook for another minute to reheat and allow the flavors to meld, with the sauce bubbling gently around the chicken.
Remove from heat, sprinkle with chopped parsley if desired, and let rest for 2 minutes. Serve the chicken hot, spooning extra sauce over each piece for a vibrant, glossy finish.
