In a large pot, add in chicken and cover with water at about half full. Add a little salt and pepper. Bring to a boil and lower to simmer for about an hour until chicken is cooked and falling off the bone.
Remove chicken and set aside to cool. Add diced onion, garlic, celery, and jalapeno to the pot. Stir well. Add two cans of diced tomatoes with chiles. Add salt, pepper, and cumin. Stir and bring to a low boil. Remove meat from chicken bones and add it back to the pot. Add chicken broth. Simmer until all vegetables are tender. Add in pre-cooked white rice. If you don't want mushy rice under cook it a little before adding to the pot. It will soften. Stir well.
Once vegetables are tender add the juice of two limes to the pot and cook for about 8 minutes. Add chopped cilantro to pot and cook for about 2 minutes. Serve soup with sliced avocado.