For the chicken: Combine all marinade ingredients together in a ziplock bag and mix around to combine. Pound chicken to 1/2 inch thickness and marinate for 1-4 hours.
While the chicken is marinating, mix up the dressings. For the chili lime vinaigrette: combine all ingredients in a mason jar, seal tightly and shake until well combined. Refrigerate. For the peanut dressing: Combine first 8 ingredients in a blender and process until smooth. Add in peanut and blend for 10 seconds more. Place in bowl or jar and refrigerate until ready to use.
Preheat grill to medium heat and cook chicken until juices run clear. Meanwhile, put the salad together. In a large bowl, combine the cabbage, lettuce, cucumber, carrot, red pepper, cilantro and green onion. Mix to combine ingredients. Once chicken has been grilled, slice into bite size chunks and place on top of salad. Scatter with wonton strips and drizzle with a good amount of chili lime vinaigrette and a bit of the peanut dressing.