Step 1: Marinate the Chicken
Place the chicken in a shallow dish or a large zip-top bag. In a small bowl, whisk together the olive oil, lemon zest, lemon juice, minced garlic, oregano, thyme, salt, pepper, and smoked paprika (if using). Pour the marinade over the chicken, ensuring it’s fully coated. Cover or seal and marinate in the refrigerator for at least 30 minutes, or ideally for 2-4 hours.

Step 2: Make the Tzatziki Sauce
While the chicken marinates, prepare the tzatziki. Grate the cucumber (you can peel it first if desired). Place the grated cucumber in a clean kitchen towel or several layers of paper towels and squeeze firmly to remove as much liquid as possible. This is crucial for a thick, non-watery sauce. In a medium bowl, combine the drained cucumber, Greek yogurt, lemon juice, olive oil, minced garlic, dill, and mint. Stir until well combined. Season with salt and pepper to taste. Cover and refrigerate for at least 30 minutes to allow the flavors to meld.

Step 3: Cook the Chicken
Heat a grill, grill pan, or large skillet over medium-high heat. Remove the chicken from the marinade (let excess drip off). Cook for 6-8 minutes per side (for breasts) or 8-10 minutes per side (for thighs), until cooked through (internal temperature of 165°F / 74°C) and nicely charred. Transfer to a cutting board, tent with foil, and let rest for 5-10 minutes. Then, slice into thin strips or bite-sized chunks.

Step 4: Warm the Pitas and Prep Toppings
While the chicken rests, warm your pitas. You can wrap them in a damp paper towel and microwave for 20-30 seconds, or heat them briefly on a dry skillet or directly over a gas flame for a few seconds per side until soft and pliable. Prepare all your fresh toppings: chop the lettuce, dice the tomato, slice the cucumber and red onion, halve the olives, and crumble the feta.

Step 5: Assemble the Wraps
Lay a warm pita flat on a plate or piece of parchment paper. Spread a generous spoonful (about 2-3 tablespoons) of tzatziki sauce down the center. Add a handful of shredded lettuce. Arrange a portion of the sliced chicken on top of the lettuce. Top with tomato, cucumber slices, red onion, Kalamata olives, and crumbled feta cheese. Add pepperoncini if desired.

Step 6: Fold and Secure
To fold, first fold the bottom edge of the pita up over the lower part of the filling. Then, fold one side over the center, and finally, roll the entire package tightly away from you, using the tucked-in bottom flap to hold everything securely. If using pocketless pitas, you can wrap the parchment paper or foil around the bottom half to hold it together for eating.

Step 7: Serve Immediately
Serve the wraps immediately, with extra lemon wedges on the side for squeezing, and a small bowl of extra tzatziki for dipping. A light drizzle of extra virgin olive oil over the filling before wrapping adds a final touch of richness.