Cook the rice according to the directions on the package. Once done, drain any excess water if necessary and season with salt and pepper. Cover with a lid and set aside.
Heat the oil in a pot over medium heat. Add in the onion, peppers, and garlic. Sauté for 3 to 4 minutes. Then add in the broth, chicken, crushed tomatoes, thyme, and oregano. Season with salt and pepper, cover with a lid and bring to a simmer for 20 minutes.
Remove the chicken from the pot, using 2 forks pull the chicken apart to shred. Then return the chicken to the pot and add the zucchini. Simmer for another 10 minutes. Taste and adjust the seasoning with salt if needed.
Ladle into bowls with rice and serve with bread. Garnish with parsley.