Preheat grill to medium-high heat. Clean grates and generously grease with vegetable oil.
Once hot, add kebabs, and grill for 4-5 minutes without moving. Flip kebabs over, brush with some Reserved Basting Marinade (that never touched the raw chicken), and grill the other side an additional 4-5 minutes.
Next, flip chicken over, baste again, COVER, and reduce heat so it maintains 400 degrees F with the lid closed. Continue to cook until the chicken reaches 165 degrees F, flipping every 5 minutes and covering (about 10-15 minutes more). Remove the kabobs from the grill and let them rest 5 minutes before carving.