Special equipment: 1 cup wood chips, soaked for at least 2 hours
Whisk the rice vinegar, canola oil, lime juice, orange juice, ancho, paprika, cinnamon, allspice, chile de arbol, ground cloves and garlic in a bowl.
Place the chicken pieces on a large baking dish. Pour the vinegar mixture over the chicken and rub it into each piece of chicken. Cover the chicken and refrigerate for at least 4 hours and up to 8 hours. Remove the chicken from the refrigerator 30 minutes before grilling.
Remove the chicken from the vinegar mixture and place on a baking sheet.
Heat a grill for indirect grilling. Add the wood chips to the coals or to a box and place on the gas briquettes. Close the grill cover and heat the grates, about 10 minutes.
Place the chicken over the direct heat, skin-side down. Grill the chicken until golden brown and slightly charred, about 5 minutes. Flip the chicken and cook 5 minutes longer. Move the chicken to the cooler part of the grill, close the grill cover and continue grilling until an instant-read thermometer inserted into the chicken registers 160 degrees F for white meat and 165 degrees F for dark meat, about 15 minutes. Transfer the chicken to a platter and loosely tent with foil.
After 5 minutes of rest, serve the chicken with the Grilled Corn, Black Bean and Quinoa Relish.
Bring 1 cup water to a boil in a small pot over medium heat. Add 1 teaspoon salt and 1/4 teaspoon pepper and stir in the quinoa. Cover the pot and cook until the quinoa is tender and the water is absorbed, about 15 minutes. Remove the pot from the heat and let sit covered. Fluff the quinoa with a fork and transfer to a large bowl.
Heat the grill to high for direct grilling. Brush the green onions with the canola oil and sprinkle with salt and pepper. Grill the onions until soft and slightly charred, about 2 minutes each side. Remove the onions from the grill and coarsely chop.
Stir the corn, beans, olive oil and lime juice in a bowl. Add the quinoa and chopped green onions. Sprinkle with salt and pepper. Keep the relish at room temperature for at least 30 minutes before serving to allow the flavors to meld. Stir in the cilantro and oregano and serve.