Working one at a time, lay pita on a plate or a piece of wax paper. Spread 1/4 cup of hummus in the center of the pita then top with 1 serving of the chicken, tomato slices, onion slices, pickle slices and pickled turnips.
Starting at the bottom, carefully fold the bottom of the pita bread over the top of the meat and other toppings. Roll tightly until pita is formed (no need to tuck in the sides.) Slice in half to serve.