Preheat outdoor or indoor grill or oven broiler.
In a medium bowl, combine cheese, tarragon, mushrooms and wine (if desired); stuff chicken breast halves with equal portions of mixture; secure with toothpicks if desired.
Brush chicken with the olive and grill/broil for 4 to 5 minutes per side then cover with foil and continue to cook for 2 minutes or until cheese melts, if needed.