In a 12-inch skillet cook mushrooms, uncovered, in 1 tablespoon of hot butter over medium-high heat about 5 minutes or until tender. Remove mushrooms from skillet.
Reduce heat to medium. Add remaining 2 tablespoons butter and the chicken breast halves to skillet. Cook, uncovered, for 8 to 12 minutes or until no longer pink (170¿ F), turning once. Remove chicken from skillet and keep warm.
Remove skillet from heat; add vinegar, stirring to loosen browned bits in bottom of skillet. Return skillet to heat.
Stir in cream, capers, and pepper. Bring to boiling; boil gently, uncovered, for 2 to 3 minutes or until sauce is slightly thickened.
Return mushrooms to skillet; heat through. Cut each chicken piece in half horizontally to make two thin pieces, if desired. Top with mushroom sauce. Serve with steamed vegetables, if desired.