In a large bowl, season the chicken with lime, salts, hot peppers, pepper flakes and black pepper. Let marinate at least 1 hour.
Heat the oil in a large pot over medium heat. Add the onion, celery and green pepper.
Cook and stir until the onion has softened and begun to brown, about 10 minutes.
Add the potatoes, carrots, red pepper flakes, allspice, bay leaves, marinated chicken, lime juice, and chicken stock.
Bring to a simmer, then reduce heat to medium-low, cover, and continue simmering until the chicken is no longer pink at the bone, and the vegetables are tender.
About 40 minutes.
Season to taste with salt and pepper before serving
with the limes half like garnish.