Slice chicken breasts in half lengthwise and pound lightly until about 1/2 inch thick.
Season both sides with salt and black pepper. Dredge lightly in flour, shaking off extra.
In a skillet over medium heat, warm 2 tablespoons olive oil. Cook chicken for 3 minutes per side until golden brown and cooked through. Remove and keep warm.
In the same skillet, add lemon juice, chicken broth, and capers. Bring to a gentle boil and scrape up browned bits.
Reduce heat, whisk in butter until sauce turns glossy.
Return chicken to pan for a quick coat in the sauce. Sprinkle parsley on top and serve warm.