Heat olive oil in a skillet with a tight-fitting lid over medium-high. Meanwhile, pat chicken dry and season with salt and pepper.Once oil is hot, add chicken to skillet and cook - without moving - for 5 minutes. Flip chicken and add the butter. Reduce heat to low and continue cooking - covered - for 10 minutes. Remove chicken along with any juices from the pan to a plate and cover with foil. Rest for 5-10 minutes.
You will need the chicken breast here to be 1-inch thick or less for this method to work best. If your chicken is thicker, you can either flatten it by pounding, or - if it's an extra hefty piece - cut it in half lengthwise. You can cook as many chicken breasts as will fit in your pan. The amount of oil/butter remains the same up to 3 chicken breasts (after that you will likely need to increase both slightly), but do use 1/4 teaspoon salt and 1/8 teaspoon pepper on each breast.