Heat coconut oil in a large frying pan over medium heat. Cook the chicken into cooked through. Transfer to a serving bowl.
Add the onions and carrots to the frying pan. Cook for 3 minutes to soften. Add the broccoli and cover. You may need to add a couple ounces of water if there isn't enough cooking liquid from the chicken. Cook the broccoli for 4-5 minutes or until desired tenderness. Transfer the veggies to the serving bowl.
Add the first 5 sauce ingredients to the frying pan and whisk. Simmer for 5 minutes. Add the chicken and veggies and toss in the sauce. Garnish with the peanuts and serve.