Cook the chicken. Coat the bottom of a 5 to 6 quart soup pot with olive oil and place it over high heat. Sprinkle both sides of the chicken breasts with salt and pepper, and place them in the pan once it's hot. After a couple of minutes, turn the heat to medium and use kitchen tongs to flip each breast over. Sauté just until they're cooked through, about 7 minutes. Set aside to cool, and do not wash the pot!
Start cooking the vegetables. While the chicken is cooling, over medium heat, in the same pot, add the onions and cook just until they're translucent, about 5 minutes. Then add the carrots and cook for a couple of minutes. Add the celery, mix and turn the heat to low. Add a couple of tablespoons of water, cover and let the vegetables steam just until they begin to soften.
Add the rice and stock. Turn the heat back to medium and add the rice. If the pan is at all dry, add more olive oil. Mix everything together to be sure the rice is coated with the oil and other ingredients. Then add the stock and bring to a boil. Immediately reduce to the lowest setting and cover until he rice is cooked and vegetables are very tender, about 15 minutes.
Shred the chicken. While the soup is cooking, use your fingers to shred the cooled chicken into bite-sized pieces.
Return chicken, add kale and season. With the heat still on low, add the shredded chicken and the kale, mix and let it cook until the kale has wilted, about 2 minutes. Now season generously to taste with salt and pepper. (Here's a Guide for Seasoning to Taste.)
Serve!