Place chicken, carrots, onion and salt in a large pot. Add enough water to cover. Bring to a boil, then reduce heat and simmer for an hour.Skim off any foam that appears, and transfer the chicken to a cutting board to cool. Remove the carrots and onion.Add rice to the broth and simmer for 20 minutes. When the chicken is cool enough to handle, tear into bite-sized pieces and discard skin and bone. Add the meat and pepper to the broth and heat through for about 3 minutes.Scoop out avocado into individual bowls and ladle the soup over the top. Sprinkle with cilantro and squeeze on the lime.Serve with chips (optional).