Blend together the oil, lemon juice, garlic, thyme, salt, and pepper. Place the chicken in a large plastic bag, pour in the lemon mixture, and seal the bag tightly. Rub gently to distribute the marinade. Marinate for at least 2 hours in the refrigerator, or all day if you wish, turning and rubbing the bag once or twice. Have a barbecue fire ready. Remove the chicken and pat it dry with paper towels; reserve the marinade. Cook 4 - 6 inches from hot coals for about 30 - 35 minutes, turning frequently. The last 10 minutes, brush two or three times with the marinade. If the chicken starts to get too dark, turn skin side up, and cover the barbecue (which will cool the fire a little) for the last 10 or 15 minutes, or move the chicken to a cooler part of the grill. Brush with the marinade as directed during last 10 minutes of cooking.