Place chicken breasts and broth in to a stockpot or Dutch oven. Bring to a boil and let simmer for about 20 minutes, or until chicken is cooked through. Remove the chicken from the broth and set aside to cool.
Put the leeks and carrots into the pot and simmer them for 10 minutes, or until tender. Shred the cooled chicken in to bite sized pieces and return it to the pot. Add the cabbage and egg noodles and cook another 5 minutes or until the noodles are soft. The soup should be thick like a stew. Serve hot and flavor to taste with Thai chili sauce.