Toss the chicken, onion, garlic, thyme, olive oil, salt, and pepper together in a bowl. Cover and refrigerate overnight.
Remove the chicken from the refrigerator 30 minutes before you start cooking. Remove the chicken from the marinade. Reserve the marinade.
Heat a large skillet over medium-high heat.
Add the olive oil to the pan, and begin browning chicken pieces in batches until golden brown. Remove the last batch from the pan, then add the allspice berries and marinade, and cook for about 5 minutes.
Add the tomatoes and return chicken to the pan. Raise the heat, and bring to a simmer. Add chicken stock, hot sauce and again, bring to a simmer. Cover pan and adjust heat to a low simmer, for approximately 30 minutes, or until chicken is cooked through. Adjust seasoning and serve.