Brown seasoned chicken breasts in butter in heavy skillet, cooking until just barely done; 8 to 10 minutes on each side. Set aside.
Pour dry vermouth in same skillet, deglazing by stirring and scraping up the browned bits from cooking the chicken, and cooking 3 minutes. Add garlic powder.
Whisk in softened cream cheese. (Add a little chicken stock or milk if you feel it is too thick – sauce should be consistency of heavy cream.) Return chicken, with any accumulated juices to the pan. Check seasoning. Spoon some sauce over chicken garnishing with green onion. Pass extra sauce.