Heat olive oil in a large pot or Dutch oven over medium-high heat. Add the onions and shallots and mix well to combine. Sauté for approximately 2-3 minutes, or until tender. Add the celery and jalapeño to the pot and stir to combine. Cook an additional 2-3 minutes, stirring often.
Reduce heat to medium and add the garlic, ground cumin, salt, pepper, and cherry tomatoes. Stir well to combine. Cook for 1-2 minutes, stirring often.
Increase heat to high. Add the low-sodium chicken broth to the pot and bring to a boil. Add the chicken breasts to the soup and covering completely with the broth. Cover the pot and reduce heat to low. Allow soup to simmer for 30 minutes.
After 30 minutes, remove the lid and carefully remove just chicken breasts from the pot onto a clean plate or cutting board. Once cool enough to handle, shred or chop the chicken breasts using two forks. Return the chicken back to the pot.
At the same time add the zucchini, green onion, cilantro, and lime juice to the pot and stir to combine. Cover and simmer for approximately 5-7 minutes, or until zucchini just starts to soften.
Remove from heat and season with additional salt, pepper, or lime juice, to taste.
Serve each bowl with chopped avocado and sour cream, cheese, and additional cilantro or green onion, if desired. Enjoy!