Whisk egg, oil, vinegar, salt, spice rub and pepper in a large bowl until well incorporated and slightly frothy.
Add chicken to marinade, ensuring all pieces are covered. Cover bowl and refrigerate for at least 3-4 hours, preferably overnight.
When ready to prepare, remove from refrigerator to bring to room temperature and preheat grill.
Remove chicken and discard any excess marinade. Grill chicken until internal temperature reaches 160°F, flipping often to prevent it from burning. Serve hot.