Place chicken breasts between two sheets of plastic wrap; pound with a mallet to an even thickness. In a shallow dish, combine flour with a generous amount of salt and pepper. Dredge chicken in the flour mixture, tapping off excess; set aside.
Heat 2 tablespoons butter and the oil in a large skillet over medium-high heat until the butter is foamy. Add chicken, and cook for 2 minutes. Turn, and cook for 2 minutes more. Remove chicken from pan, and keep warm. Pour off excess fat.
Add wine, the remaining 2 tablespoons butter, capers, and lemon juice. Cook, swirling pan to melt the butter, until reduced and slightly thickened, about 2 minutes. Pour over chicken and serve garnished with fried capers.