1. Combine 1 1/4 cups water, 1 cup bulgur, 1 tablespoon olive oil, and 1/2 teaspoon salt in a medium saucepan; bring to a boil. Reduce heat; simmer for 10 minutes (do not stir) or until the liquid almost evaporates. Remove from heat; fluff with a fork. Place bulgur in a medium bowl; let stand 10 minutes.
2. Heat the remaining 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add chicken to pan; sprinkle with 1/4 teaspoon salt and black pepper. Sauté for 4 minutes on each side or until done; shred chicken. Combine bulgur, chicken, tomato, and next 4 ingredients (through garlic) in a large bowl; toss gently.
3. Combine remaining 1/4 teaspoon salt, tahini, and remaining ingredients in a small bowl, stirring with a whisk. Drizzle over salad.