In a large saucepan combine the chicken breast, broth, and 3 cups water.
Bring the liquid to boil, and simmer the chicken, covered for 20 minutes or until cooked through.
Let the chicken cool in the broth. Transfer the chicken to a bowl reserving the broth. Discard the skin and bones. Shred the meat.
In a heavy skillet cook the onion and the garlic in 2-tbsp of oil over medium heat, stirring, until the onion is golden.
In a blender or food processor puree the mixture with the tomatoes. Stir the puree into the reserved broth with the lime juice and the peppers. Simmer the soup for 5 minutes.
Meanwhile, in the cleaned skillet, heat ¼ inch of the additional oil over medium-high heat until it is hot but not smoking.
Fry the tortilla strips in batches for 30 to 45 seconds, or until they are crisp. Transfer them as they are fried with a slotted spoon to paper towels. Add the shredded chicken and the tortilla strips to the soup.
Simmer the soup for 1 to 2 minutes, or until it is heated through. Ladle the soup into heated bowls and garnishing it with the coriander.