Rinse the chicken and pat it dry. In a large, deep, nonreactive bowl, combine the ¼ cup olive oil, lime juice, green onions, rosemary, oregano, bay leaves, chile powder, 1 teaspoon salt, and ½ teaspoon pepper and mix well. Place the chicken in the bowl and turn to coat evenly. Refrigerate for at least 4 hours and up to overnight.

Build a fire in a charcoal grill for indirect grilling over medium heat, or preheat a gas grill to medium. If using a charcoal grill, place a drip pan half full of water in the center of the fire bed. Generously oil the grill rack and position it 4-5 inches above the coals.

Remove the chicken from the bowl and discard the marinade. Place the chicken, breast side up, on the grill rack, away from the direct heat. Cover the grill and cook, rotating the chicken occasionally so that it cooks evenly on all sides, until the juices run clear when the thigh is pierced with a knife tip and the temperature registers 165°F (74°C) on an instant-read thermometer, 1½-1¾ hours. If using a charcoal grill, add more coals about halfway through the grilling. Brush the chicken with some of the Traditional Chimichurri Sauce 2 or 3 times during grilling.

Transfer the chicken to a carving board, tent with aluminum foil, and let rest, about 10 minutes. Cut the chicken into pieces and arrange the pieces on warmed individual plates. Serve right away with one or more of the chimichurri sauces.