1. Preheat oven to broil and line a baking sheet with Gefen Parchment Paper. Lay out four pitas on the parchment paper and set aside.
2. In a medium bowl, whisk together one-fourth cup BBQ sauce and half a cup mayonnaise. Set aside.
3. Pour remaining BBQ sauce into a medium sized saucepan with half a cup of water and add in chicken. Make sure chicken is covered with sauce. Bring sauce up to a boil and then to a low simmer. Cover the saucepan and allow chicken to cook until just cooked through, about 10 minutes.
4. Remove the chicken, but leave the saucepan with sauce on the stove to allow for it to thicken a bit. Set the chicken on a cutting board to rest for 10 minutes. Using two forks, shred the chicken. Return the shredded chicken to the sauce and toss to coat.
5. Spread about three tablespoons of the BBQ/mayonnaise mixture onto each pita and top with a quarter of the chicken. Repeat for remaining pitas. Broil near the heating element for three to five minutes until edges of chicken are browned.
6. Remove from oven and drizzle mayonnaise all over pita. Garnish with chopped cilantro. Serve whole or sliced into quarters.