Season chicken with salt and pepper, then dredge in flour, shaking off excess.
Heat olive oil and 1 tablespoon butter in a skillet over medium-high heat. Cook chicken until golden brown, about 3 minutes per side. Remove and set aside.
In the same skillet, add lemon juice, chicken broth, and capers. Bring to boil, scraping up brown bits from the pan.
Return chicken to skillet and simmer for 5 minutes. Remove chicken to platter.
Add remaining butter to skillet and whisk until sauce thickens. Pour sauce over chicken and serve.