Dice the onion, celery, and jalapeno (scrape the seeds out of the jalapeno before dicing). Mince the garlic. Cook the onion, celery, jalapeno, and garlic in olive oil over medium heat for about 5 minutes or until tender.
Add the chicken breast, chicken broth, canned tomatoes with chiles, oregano, and cumin to the pot. Bring the whole pot up to a boil over high heat then reduce the heat to low, place a lid on top, and let simmer for one hour.
After simmering for an hour with a lid on, carefully remove the chicken breast from the pot and use two forks to shred the meat. Return the meat to the pot. Squeeze the juice of one lime into the soup. Get as much juice as possible from the lime by using a spoon to scrape the inside of the lime.
Rinse the cilantro and then roughly chop the leaves. Add to the pot, give it a quick stir, and serve. Dice the avocado and add a few chunks to each bowl.