Heat two tablespoons of oil in a large 12-inch skillet, over medium heat.
Season the chicken with salt and pepper. Add the chicken to the hot skillet and cook for five minutes. Turn the pieces and sauté until almost cooked through, about three minutes more. Transfer the chicken to a plate and cover while you proceed with the recipe.
Add the remaining oil to the skillet and add the onion. Cook over medium-low heat until the onion softens and caramelizes, stirring often, about 20-25 minutes.
Raise the heat to medium and stir in the kale. Cook, covered, until the kale is just tender about five minutes, stirring occasionally. Cook until the tomatoes burst and the chicken is hot, about five minutes. Enjoy!