Melt butter in a nonstick skillet over medium heat; add Brussels sprouts to pan, cut side down. Cook 3 minutes, without stirring. Stir in grapes and minced garlic; cook 1 minute. Sprinkle with salt and pepper. Add 1/4 cup chicken stock; cover partially, and cook 3 minutes. Stir in vinegar and 1 tablespoon chicken stock; simmer 1 minute.
