In a large bowl, season the chicken thighs with salt, pepper, allspice, turmeric, cayenne pepper, and thyme. Rub the spices under the skin for deeper flavor.
Heat vegetable oil in a large skillet or Dutch oven over medium-high heat. Add the chicken thighs skin-side down and sear for about 5-7 minutes until golden brown. Flip and sear for another 5 minutes. Remove the chicken and set aside.
In the same skillet, add the chopped onion, garlic, ginger, and diced bell peppers. Sauté for about 3-4 minutes until the vegetables soften and the onion becomes translucent.
Stir in the rice and cook for another 2 minutes, allowing the rice to absorb the flavors and slightly toast.
Pour in the coconut milk and chicken broth. Stir well to combine and bring to a gentle simmer.
Nestle the browned chicken thighs back into the rice mixture, making sure they are partially submerged. Cover with a lid and reduce the heat to low.
Let it cook for about 30-35 minutes, or until the rice is cooked and has absorbed most of the liquid. The chicken should be fully cooked with a temperature of 165°F (74°C).
Remove from heat and let it rest, covered, for 5-10 minutes. After resting, carefully fluff the rice with a fork to combine everything together.
Plate the chicken and rice, garnishing with fresh cilantro or parsley. Serve with lime wedges on the side for an extra zing.