Melt the butter in an oven-safe pan over medium heat. Stir the garlic, lemon juice, and tarragon into the butter. Cook the chicken breasts in the butter mixture until evenly browned, 3 to 5 minutes per side. Add the olives to the pan.
Transfer the pan to the preheated oven and bake until the chicken is no longer pink in the center and the juices run clear, about 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).