1. In a 2-cup measuring cup, whisk together first 6 marinade ingredients. In a medium-size bowl, toss chicken with 1/4 cup marinade and marinate for 1 hour.
2. Heat sesame oil in a medium-size skillet over medium-high heat. Add chicken and cook, without stirring, until nicely browned on one side, 3 to 5 minutes. Stir and cook until chicken is no longer pink in the center, 5 to 8 more minutes. (If you're short on time, cook chicken immediately after tossing it with marinade.)
3. Transfer cooked chicken to a large bowl, and add remaining salad ingredients; toss to combine. Pour remaining marinade over salad and toss until everything is well coated. Cover with plastic wrap and refrigerate several hours, or overnight, to let the flavors develop.