In a large mixing bowl, combine olive oil, Greek oregano, lemon juice, lemon zest, and 1 teaspoon kosher salt. If you have time, let it sit for a bit. See tips below.
Use a good chef's knife to slice the potatoes into wedges. Season the chicken thighs on both sides with kosher salt and freshly ground black pepper.
Add the chicken and potatoes to the bowl with the Greek oregano/lemon marinade and toss to coat. Let the ingredients marinate for at least 10 minutes but no more than 30.
Spread the chicken thighs and potatoes evenly on a sheet pan along with one lemon cut into quarters.
Bake for 35-40 minutes, turning the potatoes occasionally, until the chicken skin is golden brown and the potatoes are crispy. To serve, top with crumbled feta, yogurt sauce and fresh dill. Add a lemon wedge on the side if you like.
Lemon-Dill Yogurt Sauce
While everything is cooking, make the sauce. In a small bowl, mix together the Greek yogurt, chopped dill, lemon juice and salt.