Whisk egg in a medium bowl until well beaten. Slowly add in the oil until fully blended. Then whisk in the vinegar, salt, poultry seasoning, and ground black pepper. Set aside about 1/3 of the sauce to use for basting while grilling. Place chicken in a large Ziploc bag, and coat with sauce. Seal, and marinate in the refrigerator for 24 hours.
When ready to cook:
Preheat the grill to a medium temperature, about 275 degrees F preferably over charcoal.
Arrange the coated chicken on the preheated grill. Cook (covered) for 40 to 45 minutes or until cooked through, basting with the reserved sauce after 20 minutes. Cook until internal temperature reaches 165 degrees F.
Notes
The original recipe calls for a whopping 3 tablespoons of salt, this is just way too much salt for me and my family, so I have scaled it back to 1 tablespoon.