Preheat the oven to 350 degrees F.
With a meat mallet, pound chicken breast halves until thin. Put each half on a large piece of plastic wrap and season chicken with salt and pepper, to taste.
In a saute pan over medium heat, heat 1 tablespoon oil and saute the vegetables until tender. Divide the vegetables in half and arrange in center of each chicken breast. Roll each chicken into a log and wrap tightly in the plastic wrap. Tie the ends of the wrap into a knot. Cover the bottom of a shallow baking dish with water and add the chicken. Bake until cooked through, about 20 to 30 minutes.
Meanwhile, heat a large saute pan over medium-high heat, add the remaining 1/2 cup of olive oil. When the oil is hot add the potatoes and fry until golden brown. Remove from the oil to paper towels to drain. Season with salt and pepper, to taste.
Remove the chicken from the oven to a cutting board. Discard the plastic wrap and slice. Arrange the potatoes on serving plates and top with the chicken.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.