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Preheat oven to 400 degrees.
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Mix the pesto, olive oil, Ranch seasoning, onion powder, garlic powder, salt and pepper together in a large bowl. Remove half of the combination and put it in a small bowl.
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Place cut potatoes into the bowl with the pesto and carefully stir until the pesto combination evenly coats the potatoes.
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Lightly grease a large sheet pan. (Use cooking spray, or you can also put tin foil or parchment paper in the pan).
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Place your chicken breasts on the pan and spread the reserved half of the pesto combination over the top and sides.
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Pour the potatoes on the pan around the chicken, evenly distributing them on the pan.
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Bake for 40 minutes, or until chicken reaches 165 degrees on a meat thermometer.
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Loosen the potatoes from the pan. You can serve directly from the pan, or plate the chicken and potatoes separately to put on the table.