In a large skillet over medium heat, heat the coconut oil.
To the skillet, add the chicken and onion and cook for 10 minutes. To the chicken mixture add the salt and pepper and cook for 5 minutes, until chicken is cooked through.
Remove from heat and allow to cool on the side.
In a large bowl, mix the chicken mixture with the radish, spinach and walnuts. In a small bowl whisk the remaining ingredients, (olive oil through garlic), season with salt and pepper to taste and pour over the salad and toss. Serve right away.