In bowl, combine sesame oil, chili garlic sauce, garlic, ginger, and lime juice.
Add chicken.
Cover bowl and refrigerate 2 hours, tossing once.
Remove chicken from marinade and sauté 10 minutes in skillet.
Cool chicken and slice in thin strips.
In large bowl, combine cooked chicken, cabbage, snow peas, bell pepper, and cilantro.
Refrigerate while making dressing.
In bowl, whisk together dressing ingredients.
When ready to serve, pour dressing over salad and toss.
Add salt and pepper to taste.