Cut the chicken breast into 1-inch cubes and place them in a glass mixing bowl.
In a small jar, whisk together the olive oil, lemon juice, dried oregano, garlic powder, sea salt, and black pepper to create the marinade.
Pour half of the marinade over the chicken cubes, tossing well to ensure every piece is coated; let it marinate for at least 15 minutes.
While the chicken marinates, chop the bell pepper, red onion, and zucchini into 1-inch chunks suitable for skewering.
Thread the marinated chicken and vegetable pieces onto skewers, alternating between the meat and the different colored vegetables.
Preheat a grill or a cast-iron grill pan over medium-high heat and lightly grease the surface with a touch of oil.
Place the skewers on the grill and cook for 10-12 minutes, turning every few minutes and brushing with the remaining marinade until the chicken is cooked through and the vegetables have developed a nice char.