Step 1

Cut each chicken breast that weighs more than 12 ounces in half crosswise. Put the chicken in a large bowl. In a blender, combine the cilantro, oil, oregano, garlic cloves, orange zest and juice, lime zest and juice, granulated garlic, coriander, cumin, 1 teaspoon salt and ½ teaspoon pepper. Blend on high, scraping the jar as needed, until smooth, about 1 minute. Pour ⅓ cup of the puree onto the chicken; transfer the remaining puree to a small bowl and set aside. Sprinkle the chicken with 1 teaspoon salt and rub the puree into all sides. Let stand at room temperature while you prepare the grill.

Step 2

Prepare a charcoal or gas grill. For a charcoal grill, ignite a large chimney of coals, let burn until lightly ashed over, then distribute the coals evenly over one side of the grill bed. Heat the grill, covered, for 5 to 10 minutes, then clean and oil the grate. For a gas grill, turn all burners to high and heat, covered, for 15 minutes, then clean and oil the grate; turn off one burner, leaving the remaining burner(s) on high.

Step 3

Place the chicken, skin side up, on the cooler side of the grill. Cover and cook until the thickest part of the pieces reaches 160°F, 15 to 20 minutes. Flip the chicken skin side down onto the hot side of the grill. Cook until deeply browned, about 3 minutes. Transfer the chicken skin side up to a platter and let rest for 5 minutes. Serve with the reserved puree and lime wedges.

Step 4

Oven Version: Follow the recipe to make the puree and season the chicken. Heat the oven to 375°F with a rack in the upper-middle position. While the oven heats, set a wire rack in a broiler-safe rimmed baking sheet and place the chicken, skin side up, on the rack. Roast until the thickest part of the pieces reaches 160°F, about 20 minutes. Remove from the oven and turn the oven to broil. When the broiler comes up to temperature, return the chicken to the oven and cook until the skin is browned and charred in spots, another 4 to 5 minutes. Transfer the chicken skin side up to a platter and let rest for 5 minutes. Serve with the reserved puree and lime wedges.