In a large bowl, whisk together oil, apple cider vinegar, salt, poultry seasoning and egg.
Place leg quarters in large dutch oven. Pour marinade over chicken.
Refrigerate at least 24 hours.
When ready to cook, remove chicken from refrigerator. Keep in the dutch oven and just place on your stove top. Bring to a boil over medium high heat. Turn heat down to medium and continue cooking for 10 minutes.
Remove from heat. Let sit for 10 minutes to cool. Meanwhile, pre-heat your grill for the final cook.
When grill is hot, remove chicken from marinade and discard marinade. Place chicken on grate. Cook for about 10 minutes on each side until chicken is no longer pink inside.
Notes
The oil in the marinade is not all absorbed by the chicken. This is taken into consideration when calculating nutrition.