This excellent recipe comes from the September 1988 Bon Appetit. The sauce on this chicken was so good and really not that difficult to prepare. This one is a perfect company dish.
Chicken Paillards with Basil Cream and Balsamic Vinegar
4 boneless skinless chicken breast halves
1 2-oz. piece Muenster cheese
1/2 cup loosely packed fresh basil leaves
1 medium garlic clove
2 Tbsp. extra-virgin olive oil
1/4 tsp. salt
2 Tbsp. balsamic vinegar
2/3 cup whipping cream
Salt and freshly ground black pepper
rinse chicken and pat dry. Pound each chicken breast between 2 sheets of plastic wrap to an even thickness of 1/8 inch, beginning in center and working outward.
Grate cheese and set aside. Place basil in bowl of food processor. Turn on machine. Drop garlic into feed tube and mince. Add oil and salt and mix 5 seconds. ( I found this easier to do in a small processor, the large one did not chop the mixture that well.)
Heat a 12-inch skillet over medium heat. brush one side of chicken breasts with half of basil oil. Add chicken to skillet basil side down. Brush tops with remaining oil. Cook until bottom side is just opaque, about 45 seconds. Turn and cook until second side is just opaque, about 45 seconds. Transfer to warm platter, tent with foil to keep warm.
Add vinegar to pan and scrape up any browned bits. Add cheese, cream and any collected juices from platter and stir until mixture thickens, about 2 to 3 minutes. Season with salt and pepper and spoon over chicken.