Preheat oven to 425 degrees F. In a large mixing bowl toss together the diced chicken, olive oil, and seasonings. Mix to combine and transfer to a sheet pan. Bake at 425 for 15-18 minutes flipping halfway through, or until the chicken reaches and internal temperature of 165 degrees.
For the Marinated Tomatoes:
In a large mixing bowl combine the tomatoes, the olive oil, thyme, dill, salt, and pepper. Stir to combine and allow to sit and marinate.
For the Feta:
In the bowl of a food processor or blender, combine the feta, tahini, lemon juice, and black pepper. Pulse until smooth. Add 1 tablespoon of cream at a time until the feta is smooth and creamy.
For the Pitas:
To assemble, top or stuff a warmed pita with chicken. Top with the marinated tomatoes, bacon, and a dollop of the whipped feta. Garnish with fresh herbs as desired. Leftover ingredients will keep in airtight containers in the fridge for 3-4 days.