Pre-soak wooden kabob skewers in water for a few hours before grilling.
Place chicken chunks in a large Ziploc bag. Place chopped vegetables in a separate large Ziploc bag. Set aside.
In a medium bowl, whisk together marinade ingredients. Pour half of the marinade into the bag with the chicken and the other half of the marinade into the bag with the vegetables.
Toss to coat everything in the marinade and then place bags in the refrigerator for a few hours.
Alternate threading chicken and vegetables on skewers.
Grill over medium-high heat (on an outdoor grill or on an indoor grill pan) until chicken is cooked through (about 10 minutes), turning kabobs as they cook.