Grate 1teaspoon zest and squeeze 2tablespoons juice from the lime into a small bowl. Add the oil, fish sauce, and sugar and whisk until blended.
Assemble the salad
In a large bowl, combine the chicken, cabbage, green onions, and cilantro and toss to mix well. Drizzle with the lime vinaigrette and toss to coat. Season to taste with salt and pepper. Divide among plates, top with the peanuts, and serve.