Make the marinade: Whisk together olive oil, lemon zest, lemon juice, dried thyme, dried oregano, garlic powder, kosher salt, and black pepper in a large bowl (one that is large enough to accommodate all the chicken.)
Place the cubed chicken into the bowl. Toss to make sure all of the chicken is evenly coated with the marinade.
Cover the bowl with plastic wrap, pressing down to remove any air, and seal tightly. Place it in the fridge for at least an hour but up to 12 hours.
If you use wooden or bamboo skewers, soak them in water for at least 30 minutes before cooking kabobs in the oven.
When ready to assemble, start by preheating the oven to 450 degrees F. Line a baking sheet with parchment paper and set it aside.
Loosely thread the chicken chunks on the skewer tapping off any excess marinade, and alternate with the onion and peppers. For 2 pounds of chicken, you should have 8 skewers, with each skewer having 5 pieces of cubed chicken. If your chicken is thin, you can fold it when threading on the skewer so all pieces cook evenly.
Place the kabobs on the parchment-lined baking sheet in a single layer. If desired, sprinkle them with ½ teaspoon kosher salt and ¼ teaspoon black pepper.
Bake for 16 minutes, rotating once during baking. When rotating the skewers, I recommend removing the sheet pan from the oven as it is easier (and safer) to flip the skewers, especially if you are using wooden ones.
At the end of 15 minutes, switch the oven to broil and broil* the chicken kabobs for 1 minute on each side (no more than 2 minutes total.) This step helps brown the chicken. Check for doneness by inserting a thermometer into one of the cubes. It should be done when it reaches 165 degrees F.
Remove kebabs from the oven, cover loosely with aluminum foil, and let it rest for 5 to 10 minutes. Serve.