In a large air tight container, mix together the lime, season salt, pepper, allspice and bay leaves.
Add in the chicken, stir well and marinate for 12-24 hours.
In a large dutch oven, heat the oil over medium heat
Add in the chicken pieces reserving the marinade, cook until browned on all sides, and set aside.
Add in the onions, carrots and celery, sauté until tender about 5 minutes.
Add in the potatoes and fresh thyme.
Return the browned chicken to the pot along with reserved marinade.
Add enough water to cover the chicken in the pot.
Bring to a boil and then simmer for about 45 minutes or until the chicken meat is falling off the bone.
Remove the chicken and de-bone it, adding back into the pot the chicken meat.
Add salt to taste.
Remove the allspice berries and bay leaves.
Serve with old sour, extra limes and Johnny cakes.