Move an oven rack up one level from center and preheat oven to 400°F (200°C). Spray a rimmed 18x13-inch baking sheet with nonstick spray; a dark-coated sheet helps browning.
In a small bowl, whisk together the olive oil, lemon zest, lemon juice, minced garlic, chopped thyme, chopped rosemary or oregano, and 3 tablespoons of the chopped parsley.
Place the cubed potatoes in a large bowl. Pour half of the herb mixture over the potatoes and toss to coat evenly. Season with salt and freshly ground black pepper to taste.
Spread the seasoned potatoes in an even layer on the prepared baking sheet.
Place the chicken thighs in the large bowl, pour the remaining herb mixture over them, and toss to coat. Season both sides of the thighs with salt and pepper.
Arrange the seasoned chicken thighs evenly on top of the potato layer, skin side up.
Bake in the preheated oven until the chicken is cooked through and the potatoes are tender, about 45 minutes. If desired, broil for the last few minutes to brown the skin.
If the chicken finishes before the potatoes, remove the chicken to a plate and continue baking the potatoes until soft.
Remove the pan from the oven, sprinkle the remaining parsley over the chicken and potatoes, and serve.