Preheat the oven to 400 degrees F.
Prepare the vegetables by cutting into bite-size pieces and the potatoes in small cubes.
Season the chicken with salt and pepper to taste. Sprinkle evenly over both sides of the chicken breast.
Heat the 2 tablespoons of the olive oil in a large ovenproof skillet or a cast-iron skillet. Place the chicken breast in the skillet and cook until brown on both sides about 3 to 4 minutes on both sides.
Once the chicken is browned remove it from the skillet and add 2 additional tablespoons of olive oil. Add the vegetables and saute until they start to get tender. Turning the vegetables often so they don't burn. Season with salt and pepper to taste.
Once the vegetables are ready move them around to make room for the chicken breast. Place the chicken breast back into the skillet and place the skillet in the preheated oven. Pour a cup of chicken broth into the skillet.
Roast for 20 to 25 minutes or until the potatoes are tender and the chicken is no longer pink or 165 degrees F
Remove the skillet from the oven and let the chicken rest for about 5 minutes. Serve.