While your oven preheats to 450°F, prepare two flavor mixtures. For the chicken marinade, combine 3 tablespoons olive oil with the zest and juice from 3 lemons, 4 minced garlic cloves, 2.5 teaspoons oregano, 1.5 teaspoons salt, and 0.5 teaspoon pepper in a bowl. In a separate bowl, combine 3 tablespoons olive oil with juice from 1 lemon, 2 teaspoons oregano, 1.5 teaspoons paprika, 0.5 teaspoon garlic powder, 0.25 teaspoon cayenne, 1 teaspoon salt, and 0.25 teaspoon pepper for the potatoes. Having both seasonings ready ensures you can move quickly once the oven is hot.
Add the 1.75 lb chicken thighs (cut into 1-inch chunks) to the marinade from Step 1 and let them sit for 30 minutes at room temperature—this allows the flavors to penetrate the meat. While the chicken marinates, toss the 3.5 gold potatoes (cut into 1/2-inch thick wedges) with the potato seasoning mixture from Step 1 on a foil-lined baking tray. Once the oven reaches 450°F, place the potatoes on the center rack and begin roasting.
After the potatoes have roasted for 20 minutes on the center rack, flip them and return them to the oven. At the same time, transfer the marinated chicken to a separate baking tray and place it on the top rack. I find flipping the potatoes halfway through ensures they get golden and crispy on both sides. Continue baking the chicken for 10-15 minutes until it's nearly cooked through, then continue the potatoes for another 10-15 minutes until they're tender and beginning to brown.
Slice the roasted chicken into bite-sized pieces and return it to the baking tray. Turn on the broiler and place the chicken on the top rack for 4-5 minutes to lightly char and finish cooking. While the chicken broils, drizzle fresh lemon juice over the finished potatoes from Step 3 to brighten their flavors. Remove both the chicken and potatoes from the oven and keep them warm.
While the chicken broils, prepare the yogurt sauce by combining 0.75 cup yogurt with the zest and juice from 1 lemon, 1 minced garlic clove, 2.5 tablespoons finely chopped fresh dill, 2 tablespoons water, 0.5 teaspoon salt, and 0.25 teaspoon pepper in a bowl. I always use Fage Total yogurt because it's thick and creamy, giving the sauce the right consistency without watering it down. Stir until smooth and let it sit at room temperature until serving.
Wrap the pita bread in foil and warm it in the 450°F oven for 1-2 minutes just before serving—this makes them pliable and easier to fill. Remove from the oven and fill each pita generously with the sliced chicken from Step 4, roasted potatoes from Step 4, and a generous dollop of the tzatziki sauce from Step 5. Add any additional fresh toppings like lettuce, cucumber, onion, and cheese if desired. Serve immediately while everything is still warm.