Heat a large heavy skillet to 350 degrees F about 7 minutes over medium heat on a gas range, or about 23 minutes over medium to medium-low heat on an electric range.
Place each chicken breast on a cutting board and slice horizontally to create two thin pieces. Lightly rub each piece of chicken on both sides with olive oil, salt and pepper. Place chicken in skillet and cook 3 to 4 minutes. Turn and cook other side 3 to 4 minutes. Watch for the white line coming up the sides as the chicken cooks. When it is about one-half the thickness, chicken is ready to turn.
Place the chicken on a warmed plate. Add 1 tablespoon of olive oil, peppers and onion to skillet and saute' until tender crisp.
Push onion and pepper mixture to one side of the skillet and add cooked chicken, piling the pepper mixture on each piece. Remove from heat and place 1/2 slice of Provolone cheese on each piece of chicken. Cover with a lid until cheese melts. Serve immediately.