In a large bowl, mix the olive oil, lime juice, cilantro, lime zest, salt, pepper and cayenne pepper. Add the chicken to the marinade, and toss to coat the pieces thoroughly. Cover the bowl and place it in the refrigerator for 30 minutes.
In a separate small bowl, whisk together the olive oil, lime juice, rice vinegar, sugar, lime zest, salt, crushed red pepper flakes and pepper.
In a large skillet over medium-high heat, stir-fry half the chicken mixture for four to five minutes, until the chicken is no longer pink. The interior of the chicken should be 165°F. Remove the chicken and repeat the cooking process with the next batch. Once all the chicken is cooked, set it aside to cool slightly.
In a large bowl, add the cabbage, cilantro, carrots and chicken, then toss to combine. Add the peanuts and the dressing, tossing till everything is coated. Serve the salad immediately.
