Drain artichokes, reserving 2 tablespoons marinade; set artichokes and reserved marinade aside.
Place chicken between 2 sheets of heavy-duty plastic wrap; flatten to 1/2-inch thickness, using a meat mallet or rolling pin. Combine flour, salt, and pepper in a shallow dish; dredge chicken in flour mixture, and set aside.
Melt 3 tablespoons butter in a large skillet over medium-high heat; add mushrooms, and sauté 5 minutes. Push mushrooms to one side of pan, and melt 1 tablespoon butter in pan; add chicken. Cook chicken 5 to 6 minutes on each side. Remove chicken from pan.
Add wine to skillet, and cook over medium-high heat, stirring to loosen particles from bottom of skillet. Add chicken broth, artichokes, and reserved artichoke marinade to skillet, and cook 3 minutes or until liquid is reduced by half. Remove from heat; add remaining 1 tablespoon butter and capers, stirring often until smooth. Serve sauce over chicken.