Sprinkle chicken with Greek seasoning.
Heat 1 teaspoon oil in a large nonstick skillet coated with cooking spray over medium-high heat. Add chicken; cook 2 to 3 minutes on each side or until lightly browned.
Combine chicken and roasted bell peppers in a medium bowl.
Combine 1 tablespoon oil, lemon rind, and next 4 ingredients in a small bowl. Pour marinade over chicken mixture; toss gently. Let stand 15 minutes.
Line each pita half with 1 lettuce leaf and cucumber slices. Carefully fill each pita pocket with 1/2 cup chicken mixture. Sprinkle evenly with feta cheese.