About 10-20 minutes prior to grilling, soak your skewers in hot water. This helps prevent them from catching fire. When the chicken has marinated and the skewers have soaked, thread the chicken onto the skewers.
Heat grill over medium-high heat (350-400 degrees F) and oil the grill grates (to do to this, dip a wadded paper towel in a little oil and, using tongs, wipe the oil evenly over the grate. Be careful not to use too much oil, because that's a sure fire way to start a good flare-up—a little goes a long way here.)
When hot, place the skewers on the grill and cook on the first side for 3 to 4 minutes , or until nice grill marks have formed. Flip the skewers and then baste the grilled side generously with the reserved marinade, Continue to cook until chicken is cooked through and nice grill marks have formed on both sides, 3-4 more minutes. The grill should be closed as much as possible as you are cooking the chicken.
Transfer the cooked chicken skewers to a tray and brush once more with remaining sauce, if you have any. Set aside to rest while you prepare the grilled scallions.
Drizzle the scallions with the oil. Lay the scallions on the medium-high heat grill and grill until you see girl marks, about 2 minutes. Flip the scallions and continue to cook on the other side, until you see grill marks, 1 to 2 more minutes.
To serve, slice the scallions and sprinkle over the grilled chicken skewers. Garnish with toasted sesame seeds, if desired. Serve as desired and enjoy! I served mine with grilled zucchini and steamed jasmine rice.