Cut the chicken into strips. Rub thoroughly with the jerk seasoning (wear gloves!), cover and let sit for at least 1 hour in the refrigerator.
Heat the oil in a skillet. Saute the chicken pieces until browned. Add the onion and garlic and saute for 2 to 3 minutes. Do not allow the garlic to burn.
Deglaze the pan with red wine, scraping up the slightly burned bits in the pan. Simmer for 1 minute and then add the tomatoes, tomato sauce, stock, salt and pepper. Simmer for 10 minutes uncovered, allowing the sauce to reduce and thicken. Adjust the seasoning as needed.
Meanwhile, bring a pot of water to a boil. Salt it generously and add the pasta, stirring occasionally, and cooking until al dente (see package for suggested cooking times). Drain immediately in a large colander.
Toss the hot, drained pasta with the sauce and add the basil or parsley. Sprinkle with cheese, if desired. Serve immediately.