Heat 4 tablespoons butter in a large heavy skillet over medium heat. Cook chicken breasts until golden brown, turning once. Pour in 1/2 cup vermouth. Cover, and simmer until no longer pink, and juices run clear, about 15 minutes.
In a saucepan, heat 2 tablespoons butter over medium heat. Saute onion until soft and translucent, but not brown. Stir in 1/4 cup vermouth and sour cream; remove from heat. When chicken is done, pour sauce over. Season with salt and pepper. Heat only long enough to warm the sauce, but do not boil.