In a large bowl, combine chicken pieces with fresh thyme, minced garlic, and diced onion. Cover and let marinate in the refrigerator for at least 2 hours, or overnight.

Heat oil in a large, heavy-bottomed pot over medium-high heat. Add the marinated chicken, searing until golden brown, about 5-7 minutes. Remove chicken and set aside.

In the same pot, add sliced onions, bell peppers, and minced garlic. Sauté until softened and fragrant, about 4-5 minutes.

Add the whole scotch bonnet pepper and allspice back into the pot. Pour in soy sauce and sprinkle in brown sugar, stirring to combine. Add chicken stock, bring to a simmer.

Cover pot, reduce heat to low, and braise chicken for 1.5 to 2 hours. Add chopped carrots and potatoes about 30 minutes before serving.

Once chicken is tender, taste sauce and adjust seasoning. Serve over rice or with crusty bread.