MARINATE: Whisk together soy sauce, lime juice, garlic, cumin, paprika, oregano, pepper, and oil. Put chicken in a large sealable bag and add marinade. Seal the bag and marinate in the refrigerator 8 to 24 hours.
Discard the marinade, then pat chicken dry.
Preheat the grill pan over medium-high and add the chicken. Place the chicken pieces on the pan, cooking 7 to 10 minutes per side (less if they are boneless or very thin), turning once.
Squeeze lime juice over the chicken and serve.
The chicken can be cooked on a grill, grill pan, or in the oven.GAS GRILL: Preheat the grill on high. Oil the grill rack and grill the chicken over a turned-off burner, skin side down and covered. Turn once after about 15 minutes and grill until cooked through, about 30 to 35 minutes.CHARCOAL GRILL: Open vents on bottom and lid of grill. Light a large chimney starter full of charcoal (preferably hardwood). When coals are lit, dump them out along opposite sides of bottom rack, leaving a space free of coals (the size of the quartered chicken) in middle. When you can hold your hand 5 inches above the grill rack directly over coals for 3 to 4 seconds, coals will be medium-hot. Oil the grill rack, then grill chicken over the area with no coals. Turn once after about 15 minutes, and continue grilling until cooked through, about 30 to 35 minutes. Add more charcoal to maintain heat.OVEN: Roast the chicken quarters in middle of a 500°F/260° C oven in a 13- by 9-inch roasting pan with 1 cup water for 30 minutes. Then tent with foil and roast until brown and cooked through, about 15 minutes more.