Preheat broiler. Arrange chicken, skin side down, on large rimmed baking sheet. Pour marinade over; broil 4 minutes. Turn chicken. Broil until cooked through and skin is browned, about 6 minutes.
Transfer chicken to platter. Add vermouth and cold butter to juices on sheet. Place sheet over 2 burners on medium heat. Cook until sauce is reduced to 1/2 cup, scraping up browned bits, about 2 minutes. Pour warm sauce over chicken. Serves 4