Shake marinade well. Season chicken with 1/2 teaspoon salt and 2 tablespoons of the veggie herb marinade at least 1 hour, or as long as overnight.
Marinate the veggies with the remaining marinade.
Heat a grill over medium-high, be sure grates are clean and well oiled to prevent sticking.
Put veggies on 1 large grill tray or 2 smaller trays (or cook in batches), season with 3/4 teaspoon salt and black pepper and cook, turning constantly until the edges are browned, about 8 minutes. Set aside on a platter.
Cook the chicken about 4 to 5 minutes on each side, until grill marks appear and the chicken is cooked though, transfer to a platter with the veggies and serve.