Preheat your oven to 425°F (220°C) and line a large sheet pan with parchment paper for easy cleanup.
Wash and cube the Yukon Gold potato into 1/2-inch pieces, and trim the ends of the fresh green beans.
In a small bowl, whisk together the olive oil, lemon juice, dried oregano, garlic powder, sea salt, and black pepper.
Place the potato cubes on one side of the sheet pan, drizzle with half of the lemon-herb oil mixture, and toss to coat evenly.
Roast the potatoes alone for 10 minutes to give them a head start on getting crispy.
Remove the pan from the oven, place the chicken breast in the center, and add the green beans to the remaining open space.
Drizzle the remaining herb oil over the chicken and green beans, ensuring everything is well-coated.
Return the pan to the oven and roast for an additional 15-20 minutes, or until the chicken reaches an internal temperature of 165°F.
Remove from the oven and sprinkle the fresh lemon zest over the entire dish before serving while hot.