Pound each chicken breast between two sheets of plastic wrap using a meat mallet or rolling pin until about 1/4 inch thick. This helps the chicken cook quickly and evenly while staying tender.
Place the flour in a shallow dish and season with salt and pepper. Dredge each piece of chicken in the flour, shaking off any excess for a light, even coating.
Heat the olive oil in a large skillet over medium-high heat until shimmering. Carefully place the chicken in the pan and cook until golden brown, about 2-3 minutes per side. Transfer to a plate and set aside.
Add the butter to the same skillet and let it melt. Once melted and bubbling, pour in the white wine to deglaze, scraping up any browned bits from the bottom of the pan. Let the wine reduce by half, about 2 minutes, until fragrant.
Stir in the lemon juice and lemon zest, allowing the mixture to simmer for 2 minutes until the sauce becomes glossy and slightly thickened.
Add the rinsed capers to the pan and cook for another minute, letting their briny flavor infuse the sauce. Taste and adjust seasoning with salt and pepper as needed.
Return the cooked chicken to the skillet, spooning the sauce over each piece. Cook for an additional 2 minutes to reheat and allow the flavors to meld.
Remove the skillet from heat and let the chicken rest for a minute. Plate the chicken, spooning extra sauce over the top, and garnish with additional lemon zest or parsley if desired.
Serve immediately with pasta, vegetables, or crusty bread to enjoy the bright, tangy flavors and crispy, tender chicken.
