Preheat your grill to 450° and prepare your chicken.
Toss the chicken in the oil and all the spices, coating evenly on all sides. Place the chicken on the grill and cook for 10 minutes. After 10 minutes, flip the chicken and cook an additional 5-6 minutes, or until the chicken reaches an internal temperature of 165°. Transfer the grilled chicken to a plate and allow to cool for about 10 minutes. Once cool enough to handle, slice and set aside.
Make the yogurt dill sauce. Combine all the yogurt dill sauce ingredients in a medium bowl and set aside.
Assemble your wraps. Spread the dill sauce evenly over each pita, then top with vegetables, chicken, and more dill sauce. Serve!