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Pre-heat the oven to 350. Get a large dutch oven or pot on the stove and heat the coconut oil over medium high heat. Season the chicken legs with salt. Brown the chicken pieces in two batches until they are golden on the outside. Remove them from the pot and set them aside.
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Deglaze the pot with the rum, scraping up the brown bits from the bottom. Add in the coconut balsamic and let the mixture reduce for 2-3 minutes
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Add in the shredded coconut, Worcestershire sauce, brown sugar, all spice and chicken stock. Give the braising liquid a big stir to combine it. Add the chicken back into the pot and bring it to a low boil. Cover the pot with its lid and transfer it to the oven.
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Let the coconut rum braised chicken cook for an hour and a half, until it is fall-off-the-bone tender and full of flavor. Then just plate and serve! I served it on a platter on a bed of pineapple chunks.