Whisk vinegar, oil, eggs, salt, poultry seasoning, and black pepper together in a large bowl until marinade is well mixed; add chicken. Cover bowl with plastic wrap and refrigerate, 8 hours to overnight.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Remove chicken from marinade, reserving the marinade; place on grill. Grill chicken, flipping and basting chicken with remaining marinade, until chicken is no longer pink in the center, 10 to 15 minutes per side. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).