Place chicken in a large non-reactive bowl and add onions, garlic, sliced celery, carrots, lime juice and peppers. Let chicken marinate 3 to 5 hours in the refrigerator. Strain the chicken and pat dry. Season with salt and pepper. Reserve the vegetables. Heat 2 tablespoons oil in a Dutch oven over medium heat and brown chicken on both sides. Remove chicken and pour off excess fat. Add 1 tablespoon oil to Dutch oven and saute marinated vegetables until tender, about 5 to 10 minutes. Deglaze with 2 cups chicken stock. Add chicken to Dutch oven and allow to cook over medium heat until chicken is tender and almost falling off the bone. Remove chicken and keep warm. Strain sauce through a fine sieve. Season sauce with lime zest, salt and white pepper. Warm chicken in sauce. Blanch carrots and leeks in 1 cup water with 1 tablespoon butter, salt and pepper. Serve with rice and stewed tomatoes.
In a large pot of boiling water, immerse tomatoes for about 30 to 45 seconds, or until skin easily pulls away. Transfer tomatoes to salted ice bath. Peel and seed tomatoes, quarter, or cut into thick slices over a sieve set in a bowl to catch juices.
To a small (2-quart) sauce pan, add butter, onions, tomatoes, and reserved juice. Season with salt and pepper. Bring to a boil, then reduce to a simmer, loosely cover pan, and simmer approximately 1 hour. Uncover pan, stirring constantly, raise heat until juices thicken, stirring so it doesn't burn and add fresh thyme leaves.