Preheat oven to 375 degrees F. Spray a baking dish with non-stick spray. Season chicken with salt and pepper, then place in the baking dish.
Combine chili sauce, vinegar, coconut milk, sugar, garlic, ginger, peanut butter, soy sauce and lime juice in a saucepan, whisking to combine. Bring to a boil, the reduce to a simmer and cook for 3-4 minutes until slightly thickened. Remove from heat and pour half of the sauce over the chicken, turing chicken to coat completely. Set remaining sauce aside to dress the salad with.
Bake chicken for 25-30 minutes, or until it is cooked through.
While chicken is cooking, combine all salad ingredients, except for peanuts, in a large bowl and toss. When chicken has finished cooking, let cool for a few minutes then either shred or cut into chunks. Serve salad, top with chicken, top with peanuts, then top with dressing.