In a large and deep skillet, add the oil. Heat over medium-high heat. Season the chicken generously with salt and black pepper. Add the chicken to the pan with the hot oil. Cook for 3-4 minutes on each side until cooked through and dark brown on both sides. Remove the chicken from the pan, and reduce the heat to medium-low.
If there is little to no oil left, add an additional tablespoon to the pan. Also add the caesar dressing to the pan. Swirl it around to warm up. Add the kale and season with salt and black pepper. Stir to coat with the dressing and cook for 2-3 minutes or until wilted. If you find the kale isn't wilting enough, cover it for a minute or so. This will speed up the process. Remove from heat and place the chicken back in the pan. Sprinkle with parmesan cheese and fresh parsley.
Serve immediately and enjoy!