Heat chicken in water until done (about 1 hour). Remove and cool.
Pulse onions, bell peppers, jalapeños, cilantro, and garlic in a food processor until chopped.
Add chopped vegetables, potatoes, cumin, salt, and cayenne pepper to the cooking liquid. Bring to a boil, then simmer for 45-60 minutes until potatoes are tender.
Shred the chicken and add it to the soup. Stir in lime juice and simmer for 10 minutes.
Serve with optional toppings like chopped cilantro, grated cheese, and avocados.