Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Transfer to a bowl. Return chicken and any juices to skillet. Add 1 tablespoon lemon juice. Stir until heated through, about 2 minutes.
Top pita rounds with chicken mixture.
Spoon dill sauce over chicken and serve. This sandwich is folded in half and eaten. Pass the extra sauce, as desired. All rights reserved.