Cut the chicken breasts into even-sized 1-inch cubes. Pat them dry with a paper towel. Chop the onion into quarters, then in half; cut the bell peppers into large 1-inch-square pieces, and the zucchini into ½-inch-thick rounds.
In a large bowl, mix the marinade ingredients. Add the chicken and veggies to the marinade bowl and toss to coat. Cover with plastic wrap and refrigerate for 30 minutes.
If using wooden skewers soak them while the chicken and veggies marinate to prevent them from burning on the grill by filling a sheet pan with water, spread the skewers inside, and let them soak.
Assemble:
Thread the chicken and veggies through the skewer, always poking through the middle of each ingredient to prevent it from sliding or falling off. With onions, I usually grab a couple of layers at a time. Place the assembled kabobs on a baking sheet for easy transfer to the grill. Depending on the size of your skewer, this recipe makes 6 to 8 kabobs.
Grill:
Preheat the grill with the lid closed to medium-high heat. If your grill has a temperature gauge, it should read between 375F and 400F; otherwise, preheat for 10 to 15 minutes. Use grilling tongs to grease the grates by wiping a paper towel soaked in oil over the grates. This step is especially important to prevent the skewers from sticking.
Place the kabobs on the grill across the grates (not parallel). Sear the first side with the lid open for a few minutes, then close the lid and cook for about 7 minutes. Open the grill, flip the kabobs over by picking them up from the middle using grilling tongs. Then, close the lid and cook the second side for about 5 more minutes. Total cooking time will vary depending on the thickness of the chicken pieces and your grill. Chicken breasts will need to be cooked to 165F.
Remove the kabobs from the grill to a tray, then cover them with foil to keep warm while you finish grilling.
Leftover Storage:
Remove the veggies and chicken from the skewers and store them in an airtight container. They’ll keep in the fridge for up to 4 days. To reheat, you can microwave them for about 45 seconds to 1 minute, depending how much you’re heating up. To warm them up in a pan, take them out of the fridge for 10 minutes first (so they’re not cold), drizzle a little olive oil on a non-stick pan, then heat them up over medium heat until warmed through.
Notes
Swap the fresh garlic cloves for ½ teaspoon garlic powder.
Swap the dried oregano for Italian seasoning, rosemary, or thyme.