Add chicken to a gallon-sized zipper bag. Combine marinade ingredients in a bowl and then pour over chicken. Seal bag and place in refrigerator for at least 4 hours (up to over night).
Add dressing ingredients to a mason jar. Secure lid and shake vigorously to combine. Place in refrigerator and let chill.
In a large saute pan over medium high heat, add chicken and a half cup of the marinade. Cook for 10 minutes on each side. Remove from heat and let cool on a cutting board before slicing.
In a large bowl, combine broccoli slaw, romaine mix, onions, cilantro and cucumbers. Add half of dressing, half of wonton strips and half of chopped peanuts. Toss to coat.
In a shallow bowl, add a portion of the salad mixture. Place sliced chicken to one side of bowl. Sprinkle with wonton strips. Drizzle with dressing and then sprinkle with chopped peanuts. Garnish with 2-3 lime slices