Season chicken on both sides with salt and pepper.
Heat olive oil in a heavy skillet over medium-high heat until it starts to shimmer. Place chicken breasts in skillet skin side down. Sprinkle with fresh herbs. Do not disturb the breasts until the skin side sears, 5 or 6 minutes. Turn chicken.
Cook until internal temperature reaches 150 degrees F, about 5 minutes. Add vinegar and butter to pan with chicken. Shake pan gently until butter melts and internal temperature of chicken reaches 160 to 165 degrees F, 2 to 3 minutes more. Add a splash of chicken broth or water if sauce needs to be thinned.
I used apple cider vinegar here, but literally any vinegar will work. Some of my favorites are sherry, balsamic, rice, and champagne vinegar.