Whisk all of the marinade ingredients together, EXCEPT for the olive oil, in a medium bowl. This is the "Reserved Marinade."
Put 1/4 cup of the Reserved Marinade into a gallon-size food storage bag or shallow dish. Add the chicken and 3 tablespoons of olive oil to the bag. Seal the bag (removing any excess air you can) and smush everything around to coat the chicken.
Marinate the chicken in the refrigerator for 4-6 hours.
Pour 3 tablespoons of the Reserved Marinade into a medium bowl. Whisk in the sour cream and mayonnaise to make the honey mustard dip for the kabobs. Cover and refrigerate until ready to serve.
Add the potatoes to a large microwave-safe bowl. Add 2 tablespoons water and cover. Microwave for 4-5 minutes or just until fork tender and drain any water. Add the zucchini, onions, 3 tablespoons of the Reserved Marinade, 2 tablespoons olive oil, 1/2 teaspoon salt, 1/4 pepper. Toss until evenly coated. Cover and refrigerate until the chicken is done marinating.
All of the remaining unused Reserved Marinade will be used for basting. Cover the bowl and set it aside.
After the chicken has marinated, assemble the kabobs by alternating chicken pieces and veggies on the skewers.
On the Grill
Grease the grill grates and set to medium-high heat. Grill the chicken kabobs for about 8-10 minutes. Be sure to rotate a few times until nicely browned and slightly charred on each side and the chicken is cooked through. Baste the kabobs in the remaining Reserved Marinade halfway through the cooking time.
Remove from the grill and season with salt and pepper as desired. Serve the kabobs with Honey Mustard Dip
In the Oven
Line a baking sheet with aluminum foil and lightly spray with nonstick cooking spray. Add the chicken kabobs in a single layer over the foil. Broil on high, turning every 5 minutes until cooked through, about 10-15 minutes of total cooking time( depending on the thickness of the chicken). Baste the kabobs each time you turn the chicken
Remove from the baking sheet and season with salt and pepper as desired. Serve the kabobs with Honey Mustard Dip.
Notes
If you prefer to use wooden skewers, soak them in water for 30 minutes before using them in this recipe.
You can substitute boneless skinless chicken thighs for breasts if you like.