Make the chicken marinade: In a medium bowl, whisk together the lemon zest, lemon juice, oregano, garlic, Maras pepper (or cayenne and paprika), salt, and pepper. Gradually whisk in the olive oil.
Marinate the chicken: Scoop out and set aside 1/4 cup of the marinade to use when serving. Add the chicken pieces to the bowl with the remaining marinade. Cover and refrigerate for 30 minutes, or for up to 2 hours. (Longer is better if you have time!)
Make the yogurt sauce: In a small bowl, whisk the tahini and yogurt together until smooth. Stir in 3 teaspoons of lemon juice, salt, and pepper. Taste and add more lemon juice, salt, or pepper as needed.
Cook the chicken on a grill: If using an outdoor grill, soak 6 bamboo skewers in warm water (or use metal skewers). Light a charcoal grill or turn a gas grill to medium-high. Oil the grates before grilling. Thread the chicken pieces on metal or soaked bamboo skewers while the grill is heating. Grill, turning occasionally, for 3 to 4 minutes, or until seared on the outside and cooked through to an internal temperature of 165°F. Transfer the cooked chicken to a platter and set aside.
Cook the chicken on the stovetop: Set a cast iron grill pan over medium-high heat and heat until hot. A flick of water should sizzle instantly on contact. Turn on a vent fan or open a window; the chicken will be smoky. Add a teaspoon of oil to the grill pan and swirl to coat. Working in batches if necessary, lay the chicken pieces on the hot grill pan and cook, turning often with tongs, for 4 to 6 minutes, or until seared on the outside and cooked through to an internal temperature of 165°F. Transfer the cooked chicken to a platter and set aside.
Serve: Arrange the cooked chicken on a platter with pita breads, cherry tomatoes, cucumber slices, red onion, arugula, and mint leaves. Serve with the reserved marinade and yogurt sauce on the side.