Heat the olive oil in a large pot over medium heat. Add the chopped onion and garlic, and sauté for 3-4 minutes until softened and fragrant.
- Add the sliced carrots, chopped celery, and zucchini to the pot, cooking for an additional 5-7 minutes, until the vegetables begin to soften.
- Stir in the canned diced tomatoes, chicken broth, dried basil, and dried oregano. Season with salt and pepper to taste.
- Add the chicken breasts or thighs into the pot. Bring the soup to a boil, then reduce the heat to a simmer. Let it cook for about 25-30 minutes, or until the chicken is fully cooked through.
- Remove the chicken from the pot and shred it using two forks. Return the shredded chicken to the soup.
- Add the green beans and frozen peas to the soup and cook for another 5-7 minutes, or until the vegetables are tender.
- Taste and adjust the seasoning if necessary. Garnish with fresh parsley before serving, if desired.