Heat the olive oil in a large Dutch oven over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 5 minutes. Remove the chicken and set it aside.
Add the onion, garlic, and carrots to the pot. Cook for 4 minutes until the onion softens.
Stir in the crushed tomatoes, chicken broth, oregano, salt, and pepper. Return the chicken to the pot and bring the mixture to a simmer.
Add the potatoes. Cover and simmer for 20 minutes, stirring occasionally.
Add the zucchini and continue simmering uncovered for 10 more minutes until the potatoes are tender and the sauce has thickened.