Combine the garlic, ginger, shallots, chiles, and turmeric in a food processor and pulse until the mixture is finely chopped.
Melt the coconut oil in a 10- to 12-inch heavy frying pan over medium heat. Add the chile mixture and cook, stirring frequently, until fragrant and softened, about 2 minutes. Remove the pan from heat and let cool completely.
Place the chicken pieces in a 3-quart baking dish. Squeeze the limes over the chicken and toss to coat.
Add the cooked chile mixture, the whole lime leaves, 2 tsp salt, and 1/2 tsp pepper, and using your hands, rub the mixture into the chicken until well coated. Cover the dish with plastic wrap and marinate in the refrigerator for at least 3 hours or overnight.
Remove the chicken from the refrigerator and let stand at room temperature for 30 minutes.
Arrange a rack in the top third of the oven and heat the oven to 350 degrees F. Bake the chicken, uncovered, until tender (45-50 minutes) Remove from the oven and let stand for 10 minutes. Remove the lime leaves and garnish with parsley leaves before serving.