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The night before, or at least 6 hours ahead of time, prep the chicken and the marinade. Set the chicken thighs in a rectangular dish (just big enough to accommodate the thighs). Sprinkle thighs on both sides with ½ teaspoon sea salt.
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In a medium mixing bowl, combine the lime juice, jalapeños, ginger, brown sugar, and garlic. Stir, then fold in the coconut milk. Carefully pour over the chicken thighs, cover, and refrigerate.
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When ready to make the chicken, start a hot grill. Bank the hot coals to one side to create zones of direct and indirect heat. Place marinated chicken, skin side down over the hot coals. Cook 2 - 3 minutes, flip, and cook 2 - 3 minutes more, until both sides are nicely browned. Use long tongs and be careful of flare ups. Move chicken, skin side up, over indirect heat, cover the grill, and cook until the temperature of the chicken reaches 165 degrees F.
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To make the sauce, pulse to combine the cilantro, green onions, jalapeño, garlic, lime juice, olive oil, and sea salt. Then switch the food processor on and process until smooth. Add water as needed until the mixture is smooth enough to drip off a spoon. Taste and add sea salt as needed.
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Serve chicken topped with sauce, plus more on the side. Garnish with lime wedges.