1. Preheat grill to high. Combine chicken, mint, garlic, 1/3 cup oil and 1 tsp. salt in a ziplock bag. Toss to coat. Let stand while grill heats.
2. Whisk together tahini, lemon juice, remaining 2 Tbsp. oil and remaining 1/2 tsp. salt in a small bowl until smooth. Whisk in water, 1 tablespoon at a time, until mixture has thinned to the consistency of sour cream. Sprinkle with sesame seeds, if desired.
3. Thread chicken on skewers and grill with cover closed, turning once, until cooked through, 6 to 8 minutes total. Serve with tahini sauce on the side.