Mix together the ingredients for the Cajun spice in a small bowl and set aside.
Slice the chicken into strips. Place the chicken, 2 tablespoons oil, and spices into a container or gallon-sized plastic bag and mix well. Set aside to marinade.
Heat a pot of water to a boil. Add the snap peas and cook until al dente, approximately 2 minutes. Drain and cool. Set aside
Cut the tomatoes into thin strips, reserving any dripping liquids in a small bowl. Remove the pulp and place in the small bowl. Add a tablespoon of oil into the bowl with the tomato pulp. Add salt and pepper into the small bowl and stir well to create a vinaigrette.
Heat a skillet over medium high and add the remaining oil. Add the marinated chicken and cook about 10 - 15 or until the chicken is cooked through.
While the chicken is cooking, halve and remove the pit of the avocado. Place the avocado in a bowl and mash with the lime. Add salt and pepper.
Place arugula, tomatoes, snap peas, chicken, and guacamole on plates. Serve with the tomato juice vinaigrette,