In a medium bowl, whisk 2 tablespoons oil with 1 tablespoon lemon juice, the garlic, oregano, 1 teaspoon salt, and ½ teaspoon pepper. Add the chicken thighs, and toss to coat. Let the chicken marinate for at least 30 minutes at room temperature, or up to 8 hours, covered, in the refrigerator.
Heat the oven to 425 degrees. On a sheet pan, drizzle the diced potatoes with the remaining 1 tablespoon oil and sprinkle with ½ teaspoon salt and ¼ teaspoon pepper. Toss well. Pat the chicken thighs dry and place them among the potatoes.
Roast for 15 minutes, toss the potatoes, then return everything to the oven and roast until the chicken is cooked through, the skin golden brown, and the potatoes are tender, about 25 more minutes, depending on the size of the thighs. If the potatoes are not quite tender, remove the chicken to a plate to rest, and return the potatoes to the oven to roast until tender, another 5 to 10 minutes.
Place the chicken and potatoes on a serving platter and sprinkle them with 1 tablespoon lemon juice. Scatter the feta and dill over the potatoes, and sprinkle the whole dish with salt and pepper. Serve hot.