In a bowl, whisk together olive oil, lemon juice, garlic, oregano, smoked paprika, salt, and pepper. Add the chicken and marinate for at least 30 minutes (or up to 4 hours).

Heat a skillet or grill pan over medium-high heat. Cook the chicken for 5–6 minutes per side, or until golden and cooked through. Let rest for 5 minutes, then slice.

In a separate bowl, combine Greek yogurt, feta, grated cucumber, garlic, olive oil, lemon juice, salt, and pepper. Mix until creamy and well combined.

Warm the pita breads in a dry skillet or oven.

Assemble the gyros by layering sliced chicken, tomatoes, red onion, cucumber, and a generous spoonful of feta tzatziki.

Garnish with fresh dill or parsley and serve immediately.