Preheat the oven to 425°F and line a sheet pan with parchment.
Toss potatoes with oil, salt and pepper; roast 10 minutes.
Rub the chicken with garlic, lemon zest, lemon juice, oregano, paprika and salt, including under the skin.
Nestle the chicken skin-side up among the potatoes; roast 20 minutes.
Toss green beans with oil and salt, tuck around chicken with lemon slices; roast 12 to 15 minutes more, until the chicken reads 175°F.
Rest 5 minutes, squeeze lemon over the top, sprinkle parsley, and serve.