Prepare Marinade: In a large mixing bowl, combine the plain yogurt, lemon zest, fresh lemon juice, cumin, salt, black pepper, minced garlic, and dried oregano. Whisk until well blended.

Marinate Chicken: Add the chicken pieces to the marinade, ensuring they are well-coated. Cover and refrigerate for at least 1 hour.

Prepare Tzatziki: Grate cucumber, squeeze out excess water, then mix with yogurt, minced garlic, dried oregano, dill, lemon juice, salt, and pepper.

Soak Skewers: Soak wooden skewers in water for 5-10 minutes to prevent burning during cooking.

Skewer Chicken: Thread 4-5 pieces of marinated chicken onto each skewer, leaving space for even cooking.

Cook Chicken: Bake at 400°F for 12-15 minutes or grill for 5-6 minutes on each side until fully cooked.

Serve: Let skewers rest briefly, then serve with tzatziki sauce and desired sides.