Preheat oven to broil. Line a baking sheet with foil and non-stick cooking spray.
In a small bowl, mix together the thyme, sugar, allspice, garlic powder, salt, cayenne, and pepper.
Toss the bell peppers, pineapple, and onion with olive oil. Spread them out on the baking sheet.
Rub each side of the chicken with the jerk seasoning. Place the chicken among the veggies.
Place the baking sheet in the oven for about 10-12 minutes. Flip the chicken halfway through cooking.
Remove pan from oven once chicken is cooked through and veggies are slightly charred.
Serve chicken and veggies hot from the oven with a side of rice, if desired.