Heat oil in a large stock pot over medium-high heat. Add meat, and brown evenly.
Drain off any fat or liquid rendered during browning. Add 1½ quart chicken broth and any additional broth or water to cover meat, and bring to a boil.
Reduce heat and simmer, covered, for 2 hours or until meat is tender and breaks apart, but doesn't fall apart, with moderate finger pressure.
Drain liquid from stock pot. Add remaining 2 cups of chicken stock and all other ingredients except cilantro. Simmer until peppers are tender.
Stir in cilantro, and season with salt and pepper to taste.
Serve in bowls with limes on the side.