How to Make It
Coarsely chop 2 of the onions to equal about 2 cups. Thinly slice remaining onion to equal 1 cup; set onion slices aside. Reserve any remaining onion for another use.
Place chopped onion, lemon juice, vinegar, and garlic in a blender. Process on low speed, gradually increasing speed until mixture is smooth, about 15 seconds. Stir 1 tablespoon salt into onion marinade. Transfer to a large ziplock plastic bag. Add chicken pieces to bag; seal bag, and toss to coat. Chill at least 12 hours or up to 24 hours.
Place unopened can of coconut milk in refrigerator for 15 minutes to let coconut cream thicken. Open can and spoon off thickened coconut cream (about 1 cup) from top of can, and transfer to a small saucepan. Reserve remaining coconut milk (about 2/3 cup) for rice. Place onion slices in pan with coconut cream; add tomato and 2 tablespoons chopped chiles. Bring to a boil over medium, and cook, stirring occasionally, until vegetables are tender, about 10 minutes. Remove from heat and let cool slightly. Pour mixture into blender; process until smooth, about 15 seconds. Transfer to a small serving bowl, and stir in lime juice, sugar, and remaining 2 teaspoons chopped chiles. Spoon 1/3 cup coconut-chile sauce into a small bowl, and reserve for brushing.
Place rice in a bowl and, using fingers to agitate rice, rinse under cold running water. Pour off water as it becomes opaque, and continue rinsing until water is no longer cloudy, 3 or 4 times; drain. Bring rice, 1 cup water, remaining 1 teaspoon salt, and reserved 2/3 cup coconut milk to a boil in a medium saucepan over medium-high, stirring occasionally. Cover, reduce heat to low, and simmer until liquid is absorbed, about 10 minutes. Remove from heat, and let stand, covered, until rice is tender, about 15 minutes. Fluff with a fork.
While rice stands, preheat grill. Open bottom vent of a charcoal grill completely. Light charcoal chimney starter filled with briquettes. When briquettes are covered with gray ash, pour them onto bottom grate of grill, and push to one side. Adjust vents as needed to maintain an internal temperature of 400°F to 450°F. (If using a gas grill, preheat to medium-high [400°F to 450°F] on one side.)
Remove chicken from marinade; discard marinade. Pat chicken dry, and season with a pinch of salt. Place chicken on oiled grates over side without coals (or unlit side of gas grill). Grill, covered, turning and brushing with reserved 1/3 cup coconut-chile sauce occasionally, until a thermometer inserted in thickest portion of chicken registers 165°F and skin is crispy and charred in spots, 35 to 45 minutes. Transfer chicken to a platter. If desired, season chicken with salt to taste. Serve grilled chicken with coconut rice, lime wedges, and remaining coconut-chile sauce.