Combine the chicken with the stock in a soup pot. Bring to a boil, reduce to a simmer and cook, uncovered, 30 minutes. Add the vegetables and rice and cook 20 minutes longer.
Cool the chicken in the stock. Lift out the chicken and remove and discard the skin and bones.Shred the chicken and return to the pot. Stir in the lime juice and epazote or mint and reheat the soup.Serve hot.