In large bowl, whisk tahini, lemon zest, honey, sumac, garlic, ½ teaspoon salt, and ¼ teaspoon pepper until smooth. Remove ¼ cup and set aside.
Add chicken to remaining tahini mixture and turn chicken to coat completely. Let marinate at least 1 hour or transfer to resealable plastic bag and refrigerate overnight.
Heat grill to medium and brush grates with oil. Grill chicken until instant-read thermometer registers 165°F, 7 to 8 minutes per side (discard marinade from bag).
Meanwhile, in large bowl, whisk together reserved tahini mixture, lemon juice, 2 tablespoons water, and oil.
Arrange salad greens, cucumbers, tomatoes, and chicken on platter. Drizzle with tahini dressing and sprinkle with mint.
