Cut the chicken breasts into 1-inch pieces and place in a freezer bag (gallon size).
In a bowl whisk together the chicken marinade ingredients. Pour over the chicken, seal the bag, and place in the refrigerator to marinate for 1 hour or up to 3 hours. If using wooden skewers, place the skewers in water to soak for at least 20 minutes.
In a separate bowl toss the vegetables with the vegetable seasonings.
Skewer the chicken with the vegetables in between.
Grill: when ready to grill, preheat the grill to medium-high heat, and grease the grill with oil. Cook, turning frequently, until the chicken is completely cooked through and the veggies soften.
Cast iron grill skillet: Heat a cast iron grill pan until it is hot. Lightly grease the grill pan with oil. Place the prepared skewers in a single layer. Cook, turning frequently, until the chicken is completely cooked through and the veggies soften.