Prep the chicken: Pat chicken dry.
If using breasts, pound to about 1/2–3/4 inch so they cook evenly. Thighs can be left as-is or trimmed of excess fat.
Make the marinade: In a bowl, whisk olive oil, lemon juice and zest, garlic, oregano, cumin, smoked paprika, salt, pepper, and optional yogurt. It should be fragrant and slightly thick.
Marinate: Add chicken to the marinade and toss to coat well.
Cover and chill for at least 30 minutes and up to 12 hours. Tip: Longer equals more flavor, but even 30 minutes helps.
Make the tzatziki: Combine yogurt, grated and squeezed cucumber, garlic, lemon juice, olive oil, dill, salt, and pepper. Stir, taste, and adjust. Chill until serving.
Prep toppings: Slice tomatoes, cucumbers, and red onion.
Crumble feta and chop herbs. Keep everything ready for quick assembly.
Cook the chicken (skillet): Heat a large skillet over medium-high with a light slick of oil. Cook chicken 4–6 minutes per side, until nicely browned and the center reaches 165°F (74°C).
Let rest 5 minutes.
Grill option: Preheat grill to medium-high. Grill chicken 4–6 minutes per side with the lid closed, flipping once, until cooked through. Rest before slicing.
Broiler option: Place chicken on a foil-lined sheet under the broiler on high, 5–7 minutes per side, watching closely to avoid burning.
Warm the pita: Briefly toast pitas in a dry skillet, on the grill, or wrapped in foil in a 300°F oven for 5–7 minutes so they’re soft and pliable.
Slice and assemble: Slice chicken into thin strips.
Spread warm pita with tzatziki, add chicken, tomatoes, cucumber, red onion, and feta. Finish with herbs and a squeeze of lemon.
Serve: Fold and enjoy right away. For a classic touch, wrap each gyro in parchment or foil to keep it snug and easy to eat.