Cut the chicken breast into 1-inch cubes and place them in a medium mixing bowl.
In a small jar or bowl, whisk together the olive oil, lemon juice, oregano, garlic powder, sea salt, and black pepper to create the marinade.
Pour the marinade over the chicken cubes, tossing to coat thoroughly, and let it marinate for at least 15 minutes.
While the chicken marinates, chop the red bell pepper, zucchini, and red onion into 1-inch chunks suitable for skewering.
Thread the marinated chicken and vegetable pieces onto skewers, alternating between the chicken and the different vegetables.
Preheat a grill or grill pan over medium-high heat and lightly grease with a high-heat oil if necessary.
Place the kabobs on the grill and cook for 10-12 minutes, turning every few minutes, until the chicken is cooked through and the vegetables are tender with visible grill marks.