In a large bowl, combine olive oil, lemon juice, garlic, oregano, cumin, salt, black pepper, paprika, and cayenne pepper. Add chicken pieces and toss to coat. Cover and marinate in the refrigerator for at least 30 minutes, or up to 2 hours for more flavor.
Preheat the grill to medium-high heat. Thread the marinated chicken onto skewers, leaving a little space between each piece for even cooking.
Grill the chicken skewers for about 10-12 minutes, turning occasionally, until the chicken is cooked through and has nice grill marks. The internal temperature should reach 165°F.
While the chicken is grilling, warm the pita breads on the grill for about 1-2 minutes on each side until soft and slightly charred.
In a small bowl, mix together the Greek yogurt, tahini, honey, water, and a pinch of salt and pepper. Adjust the consistency with more water if needed.
Serve the grilled chicken skewers with warm pita and a generous drizzle of the yogurt tahini sauce. Garnish with chopped parsley.