Place the cider vinegar, oil, egg, salt, poultry seasoning, and black pepper in a blender. Cover, and puree until smooth.
Pour blended mixture into a resealable plastic bag. Add the chicken halves, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator for at least 4 hours (up to overnight).
Remove chicken halves from bag and transfer to a plate or baking sheet lined with paper towels. Pat chicken dry with more paper towels. Reserve marinade mixture.
Preheat an outdoor grill for medium-high heat, and lightly oil the grate.
Grill chicken, skin-side down, on the preheated grill for 2 minutes. Turn each piece, brush with marinade mixture, and move to indirect heat.
Grill, brushing with glaze and turning often, until well-browned and meat is no longer pink in the center, about 45 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone, should read 180 degrees F (82 degrees C).