Boil the chicken breast and set aside to cool. When cooled, shred the chicken into bite size pieces.
In a sauce pan, heat the olive oil on med-high. Add the onions, pepper garlic, salt, cumin and coriander for 5 minutes, stirring regularly. Add the tomato paste and cook for 1 minute and stir. Add the chicken stock and bring to a light boil. When a light boil is achieved, lower to a simmer for 20 minutes stirring from time to time. Add the shredded chicken and simmer for 5 minutes. Add the cilantro and lime juice and stir well. remove from heat and cover to keep warm.
Some people like to add some crumbled tortilla chips to the soup when preparing to serve and well as shredded Monterey Jack cheese. Sliced avocado also goes well with it.