In a medium bowl, whisk together chicken marinade: soy sauce through Chinese five-spice powder. Add chicken breasts and marinate in the refrigerator for 30 minutes or up to overnight.
In a large resealable plastic bag, add all of the grilled vegetables ingredients (peppers through ginger.) Seal tightly and toss well to coat evenly.
When you're ready to cook, pre-heat grill to high heat. Grill the chicken breasts 5-7 minutes per side, flipping once, or until thermometer reads 165 degrees or more.
Grill vegetables in a grilling basket until tender and caramelized, tossing frequently, about 9-11 minutes. Serve with grilled chicken.