In a large bowl, combine the chicken pieces with Jamaican curry powder, salt, and pepper. Make sure the chicken is well coated and let it marinate for at least 30 minutes (or overnight for more flavor).
In a large pot or Dutch oven, heat the vegetable oil over medium heat. Add the onions, garlic, scotch bonnet pepper, thyme, allspice, and turmeric. Cook until the onions are soft and fragrant, about 5 minutes.
Add the marinated chicken pieces to the pot and brown them on all sides, about 5 minutes.
Pour in the coconut milk and chicken broth. Bring the mixture to a simmer, then reduce the heat to low. Cover and let it cook for about 40-45 minutes, stirring occasionally, until the chicken is cooked through and tender.
Taste and adjust seasoning with salt and pepper as needed.
Serve the Jamaican Curry Chicken hot over rice and peas or with roti bread. Enjoy!
