Put 2 tablespoons of the butter and 2 tablespoons of olive oil into a large skillet and place it over high heat for 2 minutes. Season the chicken breasts with a sprinkling of salt and pepper and place 4 of the breasts in the pan skin side down. Sear for 1 minute or until the skin is crispy and a golden brown. Turn the breasts and sear 1 more minute. Remove to a baking dish and repeat the process with the rest of the butter, oil and breasts. Place the baking dish into the oven for 10 to 15 minutes.
Add orange juice, chicken broth, and tarragon to the hot skillet. Cook until reduced by about 3/4 (sauce should coat the back of a spoon). Right before serving, whisk in the butter. Season with salt and pepper, to taste.
Serve the chicken with the sauce spooned over the top.