Combine lime juice, minced garlic, thyme, and allspice in a bowl, then add the chicken, turning to coat evenly. Cover and marinate in the fridge for at least 2 hours to develop flavor.
Preheat your skillet over medium-high heat and add oil. Once shimmering, carefully place the chicken skin-side down and sear for about 5-7 minutes until golden brown and crispy.
Flip the chicken using tongs, then add the sliced peppers and onions around the chicken in the pan. Pour in the coconut milk, spreading the vegetables evenly.
Reduce the heat to low, cover the skillet partially with a lid, and let everything simmer gently for about 20 minutes until the chicken is cooked through and tender, and the sauce has thickened slightly.
Uncover and squeeze fresh lime juice over the dish, then sprinkle with chopped cilantro for a burst of freshness. Taste and adjust seasoning with salt and pepper as needed.
Serve the jerk chicken hot, spooning the rich coconut sauce and vegetables over rice or alongside fried plantains for a true Caribbean experience.