Bring the polenta water to a boil over medium-high heat in a medium pot. Add the salt.
While whisking gently, pour the polenta into the boiling water in a steady stream.
Continue whisking until polenta is thickened, about five minutes. Turn down the heat to low and continue whisking until the polenta has thickened enough that it doesn't settle back onto the bottom of the pan when you stop stirring.
Once you reach that stage, cover the polenta pot and continue cooking. Stir vigorously every ten minutes or so, making sure to scrape the sides, bottom and corners of the pan.
Continue to cook for approximately 30 minutes, then stir in butter and cheese.
Meanwhile, season the chicken with salt and pepper. Heat the olive oil in a 30 centimeter skillet over medium-high heat. Add in the chicken, presentation side down and cook without moving until browned, about five minutes. Flip and brown the other side for another five minutes. Transfer to a plate.
Return the pan to medium heat and add in the onions and carrots. Cook for four minutes, then add the garlic and cook for another minute.
Add in the zucchini and thyme and mix with the onions and garlic before adding in the tomatoes, chicken stock and balsamic vinegar. Add the chicken and nestle it between the vegetables. Simmer on medium low, stirring occasionally, until the chicken reaches an internal temperature of 165 F, about 15-20 minutes.
To serve, divide the polenta between four bowls, top with the chicken tomato mixture, and garnish with minced olives and parsley.