In a large bowl, whisk the egg.
Add the vegetable oil to the egg and whisk until fully combined.
Stir in remaining ingredients until combined.
Use a fork to poke the chicken all over, allowing the marinade to get into the meat.
Place the chicken legs in a zip top bag.
Pour half of the marinade over the chicken and allow it to marinate for 3-24 hours.
Place the rest of the marinade in an air tight container or jar; refrigerate.
Grill marinated chicken over indirect heat, basting with the reserved marinade every 5-10 minutes until the internal temperature reaches 150 degrees.
Once chicken is at 150 degrees, place on direct heat and grill on all sides to crisp the skin.
When the internal temperature reaches 165 degrees, remove from the heat.