Make the dressing: in a small bowl, combine the peanut butter, rice vinegar, soy sauce, lime juice and finely chopped chilli. Set aside.
Heat the sesame oil in a wok, add the cabbage and stir-fry for 1 minute before adding the noodles and stir-frying for a further minute.
Remove from the heat and toss through the spinach, red pepper and carrot.
Divide between 4 plates. Top with the chicken, sliced chilli and lime zest. Drizzle over the peanut dressing and serve with the lime wedges for squeezing over.