Heat 1 Tbsp oil in a large non-stick skillet over medium-high heat. Add chicken and saute 3 1/2 - 4 minutes, or until cooked through, tossing occasionally.
Transfer chicken to a plate, add remaining oil and repeat with remaining chicken. While chicken is cooking, whisk together teriyaki sauce, water, cornstarch and honey, set aside.
Heat remaining 1/2 Tbsp oil in same skillet over medium-high heat. Add garlic and 3/4 cup green onions and saute 20 seconds.
Add bell pepper and water chestnuts and saute 2 minutes. Whisk sauce mixture once more and pour into skillet.
Cook, stirring constantly, 1 minute. Add chicken, leaving excess juices on plate, and carrots, toss and let warm through.
Serve over lettuce leaves with remaining 1/4 cup green onions.