Combine first 6 ingredients in a large bowl; stir in 1 tablespoon yogurt, 1 tablespoon juice, and 2 garlic cloves. Add chicken; toss to coat. Heat oil in a large nonstick skillet over medium-high heat. Add chicken mixture to pan; sauté 6 minutes or until browned and done, stirring frequently.
While chicken cooks, combine remaining 1/4 cup yogurt, remaining 1 tablespoon lemon juice, remaining 1 garlic clove, and tahini, stirring well. Spread 1 1/2 teaspoons tahini mixture inside each pita half; divide chicken evenly among pita halves. Fill each pita half with 1 tablespoon cucumber, 1 tablespoon tomato, and 1 1/2 teaspoons onion.