In a large pot heat olive oil over medium-high heat. Stir in onions, celery, and jalapeños. Sauté until tender.
Add garlic. Stir and cook until fragrant, about 1 minute.
Add whole chicken breasts, chicken broth, tomatoes, oregano, and cumin. Bring to a boil and reduce heat to a simmer. Cover pot and simmer for 45 minutes, periodically stirring.
Once the chicken is fully cooked, remove from pot and shred using two forks. Return to soup.
Add lime juice and season with salt and pepper.
Stir in cilantro. Garnish with avocado right before serving.