Cut the chicken into 1-inch cubes. Heat a large, non-stick skillet over medium-high heat, about 3 minutes. Add 1/2 tablespoon coconut oil and allow it to melt. Brown the chicken – cooking in batches, if necessary – until golden all around, about 3-5 minutes per side. Remove the chicken from the pan as it browns and place in a bowl to catch the juices.
To the pan, add 1/2 tablespoon coconut oil. Sauté the onions, peppers, and arrowroot until the vegetables are just-tender, about 5 minutes. Add the pineapple chunks to the pan and stir-fry until they begin to brown, about 3 minutes. Add the garlic and Jerk Seasoning, stirring until fragrant, about 30 seconds. Add the lime juice and stir, scraping up any brown bits stuck to the bottom of the pan. Add the vanilla and coconut milk, stirring to combine. Place the chicken in the sauce and pour in any accumulated juices. Bring to a boil, then simmer, uncovered, until the sauce begins to thicken, about 5 minutes.