In a large pot heat 1 Tbsp olive oil over medium heat.
Once hot, add green onions and jalapenos and sauté until tender, about 2 minutes, adding garlic during last 30 seconds of sautéing.
Add chicken broth, tomatoes, cumin, season with salt and pepper to taste and add chicken breasts. Bring mixture to a boil over medium-high heat. Then reduce heat to medium, cover with lid and allow to cook, stirring occasionally, until chicken has cooked through 10 - 15 minutes (cook time will vary based on thickness of chicken breasts).
Reduce burner to warm heat, remove chicken from pan and let rest on a cutting board 5 minutes, then shred chicken and return to soup.
Stir in cilantro and lime juice.
Add avocados to soup just before serving (if you don't plan on serving the soup right away, I would recommend adding the avocados to each bowl individually, about 1/2 an avocado per serving).
Serve with tortilla chips, cheese and sour cream if desired.