Heat olive oil in a large skillet over medium-high heat. Season chicken breasts with salt and pepper. Cover both sides with flour.
Add chicken to hot skillet and cook until browned on both sides and fully cooked, about 2-3 minutes per side. Remove from pan and keep warm. Work in batches, if needed, until all of the chicken is cooked.
Reduce heat to medium-low and add butter to the skillet. Melt and stir frequently, making sure to scrape up any bits left on the skillet from the chicken. Cook over medium-low heat for about 5 minutes, until the butter starts browning.
Add the capers, lemon juice, and wine or chicken stock. Cook for another 3-5 minutes. Watch it closely so that the butter does not burn.
Spoon the brown butter and capers over the chicken and serve.